{"id":311,"date":"2022-04-13T10:38:43","date_gmt":"2022-04-13T10:38:43","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=311"},"modified":"2025-03-03T10:09:46","modified_gmt":"2025-03-03T10:09:46","slug":"p-6-perimeters-of-similar-figures","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/p-6-perimeters-of-similar-figures\/","title":{"rendered":"P.6 Perimeters of similar figures"},"content":{"rendered":"\n

Perimeters of similar figures<\/strong><\/h2>\n\n\n\n

Key Notes :<\/p>\n\n\n\n

The following proportion applies to similar shapes:<\/p>\n\n\n\n

a\/b=p1<\/sub>\/p2<\/sub><\/p>\n\n\n\n

where a\/b is the ratio of the corresponding side lengths, and p1<\/sub>\/p2<\/sub> is the ratio of the perimeters.<\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

The figures below are similar. The labelled sides are corresponding.<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the perimeter of the smaller hexagon?<\/strong><\/p>\n\n\n\n

P<\/em>2<\/sub> = _________ millimetres<\/p>\n<\/div><\/div>\n\n\n\n

Find the ratio of the corresponding side lengths.<\/p>\n\n\n\n

a \/ b = 8\/4 =2\/1<\/p>\n\n\n\n

Find the ratio of the perimeters.<\/p>\n\n\n\n

p1<\/sub> \/ p2<\/sub> = 48 \/ p2<\/sub> <\/p>\n\n\n\n

Use these two ratios to set up a proportion and solve for P<\/em>2.<\/p>\n\n\n\n

2 \/ 1 = 48 \/ p2<\/sub> <\/p>\n\n\n\n

2 \/ 1 (p2<\/sub>) = 48 \/ p2<\/sub> (p2<\/sub>) Multiply both sides by <\/em>P2<\/em><\/p>\n\n\n\n

2 p2<\/sub> = 48 .1 Simplify<\/em><\/p>\n\n\n\n

2 p2<\/sub> = 48 Simplify<\/em><\/p>\n\n\n\n

2 p2<\/sub> \u00f7  2= 48 \u00f7 2 Divide both sides by 2<\/em><\/p>\n\n\n\n

p2<\/sub> = 24<\/p>\n\n\n\n

The perimeter of the smaller hexagon is 24 millimetres.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

The figures below are similar. The labelled sides are corresponding.<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the perimeter of the smaller rectangle?<\/strong><\/p>\n\n\n\n

P<\/em>1<\/sub> = _________ millimetres<\/p>\n<\/div><\/div>\n\n\n\n

Find the ratio of the corresponding side lengths.<\/p>\n\n\n\n

a \/ b = 2\/6 =1\/3<\/p>\n\n\n\n

Find the ratio of the perimeters.<\/p>\n\n\n\n

p1<\/sub> \/ p2<\/sub> = p1<\/sub> \/ 30<\/p>\n\n\n\n

Use these two ratios to set up a proportion and solve for p1<\/sub>.<\/p>\n\n\n\n

1 \/ 3 = p1<\/sub> \/ 30<\/p>\n\n\n\n

1 \/ 3 (3 . 30) = p1<\/sub> \/ 30 (3 . 30) Multiply both sides by <\/em>3 . 30<\/p>\n\n\n\n

1 .30 = 3 p1<\/sub> Simplify<\/em><\/p>\n\n\n\n

30 = 3 p1<\/sub> Simplify<\/em><\/p>\n\n\n\n

30 \u00f7  3= 3 p1<\/sub> \u00f7 3 Divide both sides by <\/em>3<\/p>\n\n\n\n

10 = p1<\/sub><\/p>\n\n\n\n

The perimeter of the smaller rectangle is 10 centimetres.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

The figures below are similar. The labelled sides are corresponding.<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the perimeter of the smaller pentagon?<\/strong><\/p>\n\n\n\n

P<\/em>2<\/sub> = _________ millimetres<\/p>\n<\/div><\/div>\n\n\n\n

Find the ratio of the corresponding side lengths.<\/p>\n\n\n\n

a \/ b = 9\/5<\/p>\n\n\n\n

Find the ratio of the perimeters.<\/p>\n\n\n\n

p1<\/sub> \/ p2<\/sub> = 45 \/ p2<\/sub> <\/p>\n\n\n\n

Use these two ratios to set up a proportion and solve for P<\/em>2.<\/p>\n\n\n\n

9 \/ 5 = 45 \/ p2<\/sub> <\/p>\n\n\n\n

9 \/ 5 ( 5p2<\/sub>) = 45 \/ p2<\/sub> (5p2<\/sub>) Multiply both sides by <\/em> 5p2<\/sub><\/p>\n\n\n\n

9 p2<\/sub> = 45 .5 Simplify<\/em><\/p>\n\n\n\n

9 p2<\/sub> = 225 Simplify<\/em><\/p>\n\n\n\n

9 p2<\/sub> \u00f7  9 = 225 \u00f7 9 Divide both sides by <\/em>9<\/p>\n\n\n\n

p2<\/sub> = 25<\/p>\n\n\n\n

The perimeter of the smaller pentagon is 25 millimetres.<\/p>\n<\/div><\/div>\n\n\n\n

Let’s practice!<\/p>\n\n\n\n

\n
\n
\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
\n
\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Perimeters of similar figures Key Notes : The following proportion applies to similar shapes: a\/b=p1\/p2 where a\/b is the ratio of the corresponding side lengths, and p1\/p2 is the ratio of the perimeters. Learn with an example The figures below are similar. The labelled sides are corresponding. What is the perimeter of the smaller hexagon?Continue reading “P.6 Perimeters of similar figures”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-311","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/311","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=311"}],"version-history":[{"count":17,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/311\/revisions"}],"predecessor-version":[{"id":17558,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/311\/revisions\/17558"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}