# Areas of two similar triangles are 36 cm2 and 100 cm2. If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle. - Mathematics

Sum

Areas of two similar triangles are 36 cm2 and 100 cm2. If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle.

#### Solution

Given, area of smaller triangle = 36 cm2 and area of larger triangle = 100 cm2

Also, length of a side of the larger triangle = 20 cm

Let length of the corresponding side of the smaller triangle = x cm

By property of area of similar triangle,

(ar("larger triangle"))/(ar("smaller triangle")) = ("Side of larger triangle")^2/("Side of smaller triangle"^2)

⇒ 100/6 = (20)^2

⇒ x^2 = ((20)^2 xx 36)/100

⇒ x^2 = (400 xx 36)/100 = 144

∴ x = sqrt(144) = 12 cm

Hence, the length of corresponding side of the smaller triangle is 12 cm.

Concept: Similarity of Triangles
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 6 Triangles
Exercise 6.3 | Q 12 | Page 69
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