{"id":188381,"date":"2025-02-06T19:47:33","date_gmt":"2025-02-06T19:47:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188381"},"modified":"2025-02-06T19:47:35","modified_gmt":"2025-02-06T19:47:35","slug":"a-is-a-scale-image-of-figure-b","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/06\/a-is-a-scale-image-of-figure-b\/","title":{"rendered":"A is a scale image of figure B"},"content":{"rendered":"\n<p>A is a scale image of figure B. Figure A x Figure B 12 2 Figure A maps to figure B with a scale factor of 7 of \uc544 What is the value of x?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-107.png\" alt=\"\" class=\"wp-image-188382\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>n the given problem, we have two similar figures, A and B, with a scale factor of 7. This means that each corresponding side of figure A is 7 times the length of the corresponding side of figure B.<br><strong>Understanding Scale Factor and Its Implications:<\/strong><\/p>\n\n\n\n<p>he scale factor between two similar figures is the ratio of their corresponding side lengths. If the scale factor is 7, then for any corresponding sides ( a ) and ( b ) of figures A and B respectively, the relationship is:<br>[ \\frac{a}{b} = 7 ]<\/p>\n\n\n\n<p>his implies that each side of figure A is 7 times longer than the corresponding side of figure B.<br><strong>Calculating the Ratio of Areas:<\/strong><\/p>\n\n\n\n<p>he ratio of the areas of two similar figures is the square of the scale factor. Therefore, if the scale factor is 7, the ratio of the areas ( A_{\\text{A}} ) and ( A_{\\text{B}} ) of figures A and B is:<br>[ \\frac{A_{\\text{A}}}{A_{\\text{B}}} = 7^2 = 49 ]<\/p>\n\n\n\n<p>his means that the area of figure A is 49 times the area of figure B.<br><strong>Calculating the Ratio of Volumes:<\/strong><\/p>\n\n\n\n<p>or three-dimensional figures, the ratio of volumes is the cube of the scale factor. Thus, if the scale factor is 7, the ratio of the volumes ( V_{\\text{A}} ) and ( V_{\\text{B}} ) of figures A and B is:<br>[ \\frac{V_{\\text{A}}}{V_{\\text{B}}} = 7^3 = 343 ]<\/p>\n\n\n\n<p>herefore, the volume of figure A is 343 times the volume of figure B.<br><strong>Application to the Given Problem:<\/strong><\/p>\n\n\n\n<p>he problem states that figure A maps to figure B with a scale factor of 7. If we are tasked with finding the value of ( x ) in the equation:<br>[ \\text{Figure A} \\times \\text{Figure B} = 12 \\times 2 ]<\/p>\n\n\n\n<p>e can interpret this as the product of the areas of figures A and B. Given that the area of figure A is 49 times the area of figure B, we can set up the equation:<br>[ 49 \\times A_{\\text{B}} = 12 \\times 2 ]<\/p>\n\n\n\n<p>Solving for ( A_{\\text{B}} ):<\/p>\n\n\n\n<p>[ A_{\\text{B}} = \\frac{12 \\times 2}{49} = \\frac{24}{49} ]<\/p>\n\n\n\n<p>herefore, the area of figure B is ( \\frac{24}{49} ) square units.<br><strong>Conclusion:<\/strong><\/p>\n\n\n\n<p>n summary, when two figures are similar with a scale factor of 7, the ratio of their areas is 49:1, and the ratio of their volumes is 343:1. These relationships are fundamental in geometry and are crucial for understanding the properties of similar figures.<br>For a visual explanation of how to find the scale factor with similar figures, you might find the following video helpful:<\/p>\n\n\n\n<p>\ue200video\ue202How to Find Scale Factor with Similar Figures\ue202turn0search6\ue201<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A is a scale image of figure B. Figure A x Figure B 12 2 Figure A maps to figure B with a scale factor of 7 of \uc544 What is the value of x? The Correct Answer and Explanation is : n the given problem, we have two similar figures, A and B, with [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-188381","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188381","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=188381"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188381\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}