Areas of two similar triangles are $36\ cm^2$ and $100\ cm^2$. If the length of a side of the larger triangle is $3\ cm$, then find the length of the corresponding side of the smaller triangle.

Given: Areas of two similar triangles are $36\ cm^2$ and $100\ cm^2$. If the length of a side of the larger triangle is $20\ cm$.

To do: To find the length of the corresponding side of the smaller triangle.

Solution:

As given, area of smaller triangle $=36\ cm^2$

Area of larger triangle $=100\ cm^2$

Length of the side of the smaller triangle $=3\ cm$

Let $x\ cm$ length of the corresponding side of the larger triangle.

As known,

$\frac{area( larger\ triangle)}{area( smaller\ triangle)}=\frac{( side\ of\ larger\ triangle)^2}{( side/ of/ smaller/ triangle)^2}$

$\frac{100}{36}=\frac{x^2}{3^2}$

$\Rightarrow 36x=100\times3^2$

$\Rightarrow x^2=\frac{900}{36}$

$\Rightarrow x^2=25$

$\Rightarrow x=\pm\sqrt{25}$

$\Rightarrow x=\pm5$

$\because$ Side of a triangle can't be negative. 

Thus, the corresponding side of the smaller triangle is $5\ cm$.

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Updated on: 10-Oct-2022

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