Areas of two similar triangles are 36 cm2 and 100 cm2.

Question:

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,

$\frac{\operatorname{ar}(\text { larger triangle })}{\operatorname{ar}(\text { smaller triangle })}=\frac{(\text { Side of larger triangle })^{2}}{\text { Side of smallertriangle }^{2}}$

$\Rightarrow$ $\frac{100}{36}=\frac{(20)^{2}}{x^{2}} \Rightarrow x^{2}=\frac{(20)^{2} \times 36}{100}$

$\Rightarrow$ $x^{2}=\frac{400 \times 36}{100}=144$

$\therefore$ $x=\sqrt{144}=12 \mathrm{~cm}$

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

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