Question

The areas of two similar triangles are 20m2 and 180m2. The length of one of the sides of the second triangle is 12m. What is the corresponding side of the first triangle?

Answer 1

4 m.

Explanation:

The ratio of the sides = ratio of the square roots of the areas.

Ratio of the sides = √ 20 / √180

= 2√5 / 6 √5

= 1/3

So the length of the required side = 1/3 * 12

= 4

Answer 2

The corresponding side of the first triangle is 4 m.

Explanation:

In similar triangle, ratio of areas of triangles is equal to the ratio of square of their corresponding sides.

Consider, the below two similar triangles,

area(ΔXYZ) = 20m² , area(ΔPQR) = 180m² and PQ = 12m

We have to find value of XY.

According to above property of similar triangle,

`\frac{ar(\bigtriangleup{XYZ})}{ar(\bigtriangleup{PQR})}=((XY)^2)/((PQ)^2)`

Put values in the above equation, we get,

`(20)/(180)=((XY)^2)/((12)^2)`

Solving for XY,

`\Rightarrow (1)/(9)=((XY)^2)/(144)`

Cross multiply, we get,

`\Rightarrow (144)/(9)=(XY)^2`

`\Rightarrow \sqrt{(144)/(9)}=(XY)`

`\Rightarrow (12)/(3)=XY`

`\Rightarrow XY=4`

Thus, the corresponding side of the first triangle is 4 m.