Question

∆ PQR ~ ∆ XYZ PQ XY= 7:3 then find A ( ∆ PQR) : A ( ∆ XYZ)​

Answer 1

Step-by-step explanation:

Given:-

∆ PQR ~ ∆ XYZ and PQ: XY= 7:3

To find:-

find A ( ∆ PQR) : A ( ∆ XYZ)

Solution:-

Given that ∆ PQR ~ ∆ XYZ

∆ PQR and ∆ XYZ are similar triangles

and given that

PQ: XY= 7:3

We know that

" The ratio of the areas of the two similar triangles is equal to the ratios of the two squares of the corresponding sides".

∆ PQR ~ ∆ XYZ

=> A ( ∆ PQR) / A ( ∆ XYZ)

=>(PQ/XY)^2 = (QR/YZ)^2 = (PR/XZ)^2

=>(7/3)^2

=>7^2/3^2

=>(7×7)/(3×3)

=>49/9

Area ( ∆ PQR) :Area ( ∆ XYZ) = 49:9

Answer:-

Area ( ∆ PQR) :Area ( ∆ XYZ) = 49:9

Used formula:-

• The ratio of the areas of the two similar triangles is equal to the ratios of the two squares of the corresponding sides.