Question

Areas of 2 similar triangles are 392 and 200 then the ratio of a pair of corresponding sides is

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The Ratio of a pair of corresponding side is 7 : 5

Step-by-step explanation:

Given: Area of similar triangles are 392 and 200 unit²

To find: ratio of a pair of corresponding sides.

Let Two similar triangles be ΔABC and ΔXYZ

⇒ Area of ΔABC = 392 unit² & Area of ΔXYZ = 200 unit²

Ratios of Corresponding Sides of similar triangle are,

$\frac{AB}{XY}=\frac{CB}{ZY}=\frac{AC}{XZ}$

We use the result which states that if a two triangle are similar than the ratio of there area is equal to square of the ratio of their corresponding sides.

⇒ $\frac{ar\,\Delta ABC}{ar\,\Delta XYZ}=\frac{AB^2}{XY^2}=\frac{CB^2}{ZY^2}=\frac{AC^2}{XZ^2}$

Consider,

$\frac{ar\,\Delta ABC}{ar\,\Delta XYZ}=\frac{AB^2}{XY^2}$

$\frac{392}{200}=(\frac{AB}{XY})^2$

$\frac{AB}{XY}=\sqrt{\frac{392}{200}}$

$\frac{AB}{XY}=\sqrt{\frac{49}{25}}$

$\frac{AB}{XY}=\frac{7}{5}$

Therefore, The Ratio of a pair of corresponding side is 7 : 5