Question

triangle abc is congruent to triangle pqr a (triangle abc)=16 a(triangle pqr)=25 then find the vale ab/pq​

Answer 1

Step-by-step explanation:

Given:

∆ABC ∽ ∆PQR

Area of ∆ABC = 16

Area of ΔPQR = 25

To find:

The value of the ratio of AB:PQ

Solution:

Since we are given that ΔABC and ΔPQR are similar to each other, so we can state the following theorem:

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

here,

AB and PQ are the corresponding sides of the similar triangles

∴ area of triangle abc / area of triangle pqr

{ab/pq}^2

substituting the given values of area of ΔABC & area of ΔPQR

⇒ 16/23 = {ab/pq}^2

taking square root on both sides

⇒ √ 16/25 =√ ab/pq^2

⇒ 4/5 = ab/pq

⇒ AB :PQ

Thus, the value of ratio of AB : PQ is 4 : 5.

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