Question

the ratio corresponding side of tow similar traingle is 4:7find the ratio of the area of their area​

Answer 1

Correct Question:

The ratio of corresponding sides of two similar triangle is 4:7. Find the ratio of areas of their similar triangle.

Solution:

Let us denote the ratio of first and other side of the similar triangle as $\tt{(S_1)\:and\:(S_2)}$ where, S is denoted as Side.

According to theorem of area of similar triangles,

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

To know the concept of Theorem better, let us consider two similar triangles: $\tt{\triangle ABC\:and\: \triangle PQR}$ Then, we can say that:

⟶$\tt{\dfrac{ar(ABC)}{ar(PQR)} = \dfrac{AB^2}{PQ^2} = \dfrac{BC^2}{QR^2} = \dfrac{CA^2}{RP^2}}$

Now, let us come to the problem. According to the question:

$⟶\tt{ar(First\:Triangle):ar(Second\:Triangle) = (S_1)^2:(S_2)^2}$

$⟶ \tt{ar(First\:Triangle):ar(Second\:Triangle) = (4)^2:(7)^2}$

$⟶ \boxed{\tt{ar(First\:Triangle):ar(Second\:Triangle) = 16:49}}$

From this, Let us conclude this problem:

$\tt{Ratio\:of\: required \:areas = 16:49}$