Question

The diagram shows two mathematically similar triangles, T and U.
Two corresponding side lengths are 3 cm and 12 cm.
The area of triangle T is 5 cm2
.
Find the area of triangle U.

Answer 1

Given:

The diagram shows two mathematically similar triangles, T and U.

Two corresponding side lengths are 3 cm and 12 cm.

The area of triangle T is 5 cm²

To find:

The area of triangle U.

Solution:

We know that,

The ratio of the areas of the two similar triangles is equal to the ratio of the square of their corresponding sides.

$\Rightarrow \boxed{\bold{\frac{Area\:(Triangle\: 1)}{Area\:(Triangle\:2)} = \bigg(\frac{Corresponding \:side\:of \:\triangle 1}{Corresponding \:side\:of \:\triangle 2} \bigg)^2 }}$

Here we have

Δ T ~ Δ U

The lengths of the two corresponding side are 3 cm and 12 cm

Area (Δ T) = 5 cm²

Now, by using the above theorem, we get

$\frac{Area\:(\triangle\: T)}{Area\:(\triangle\:U)} = \bigg(\frac{Corresponding \:side\:of \:\triangle T}{Corresponding \:side\:of \:\triangle U} \bigg)^2 }}$

on substituting the given values, we get

$\implies \frac{5}{Area\:(\triangle\:U)} = \bigg(\frac{3}{12} \bigg)^2 }}$

$\implies \frac{5}{Area\:(\triangle\:U)} = \frac{9}{144}$

$\implies Area\:(\triangle\:U) = \frac{144 \times 5}{9}$

$\implies \bold{Area\:(\triangle\:U) = 80\:cm^2}$

Thus, the area of Δ U is → 80 cm².

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