Question

triangle ABC is similar to triangle PQR area of triangle ABC = 16 area of triangle PQR =25 then find the value of the ratio AB/PQ​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given:

Triangle ABC is similar to triangle PQR

Area of triangle ABC = 16

Area of triangle PQR =25

To Find:

find the value of the ratio AB/PQ​

Solution:

Theorem:

The ratio of the area of the two similar triangles is equal to the ratio of the squares of the corresponding sides of similar triangles .

So, By theorem:

$\frac{\text{Area of triangle ABC}}{\text{Area of triangle PQR}}=\frac{AB^2}{PQ^2}\\\Rightarrow \frac{16}{25}=\frac{AB^2}{PQ^2}\\\Rightarrow \sqrt{\frac{16}{25}}=\frac{AB}{PQ}\\\Rightarrow \frac{AB}{PQ}=\frac{4}{5}$

Hence  the value of the ratio AB/PQ​ is 4:5