Question

△ABC ~ △PQR. A(△ABC) : A (△PQR) = 16 : 25. If BC = 2 cm, find QR.​

Answer 1

Step-by-step explanation:

△ABC ~ △PQR.

Area(△ABC) : Area (△PQR) = 16 : 25.

IBC = 2 cm

A(△ABC) : A (△PQR) = BC^2:QR^2

16:25 = 2^2:QR^2

QR^2= 25 X 4/16

QR= 25/2

=12.5cm

Answer 2

Given:

A(△ABC) : A (△PQR) = 16 : 25

△ABC ~ △PQR

To find:

The length of QR

Solution:

The length of QR is 2.5 cm.

We can find the length by following the given steps-

We know that the ratio of the areas of two similar triangles is equal to the ratio of the square of corresponding sides.

We are given that △ABC ~ △PQR.

The corresponding sides of both the triangles are AB-PQ, BC-QR, AC-PR.

So, the ratio of the areas of the two triangles will be equal to the ratio of the squares of these sides.

AB/PQ=BC/QR=AC/PR

The area of (△ABC): area of (△PQR)= 16: 25

Ar(△ABC)/Ar(△PQR)=16/25

We know that Ar(△ABC)/Ar(△PQR)=$(AB/PQ)^{2}$=$(BC/QR)^{2}$=$(AC/PR)^{2}$

We are given that BC=2 cm.

So, Ar(△ABC)/Ar(△PQR)=$(BC/QR)^{2}$

On putting the values, we get

16/25=$(BC/QR)^{2}$

4/5=2/QR

QR=5×2/4

QR=2.5 cm

Therefore, the length of QR is 2.5 cm.