Question

Q3
The area of similar triangles, XYZ and
PQR are 144 cm- and 64 cm?
respectively. If the longest side of the
triangle XYZ is 36 cm, then the longest
side of the triangle PQR is:​

Answer 1

ANS:24

I HOPE IT HELPS YOU

Answer 2

Answer:

The length of the longest side of the ΔPQR is 24cm.

Step-by-step explanation:

Given two similar triangles, ΔXYZ and ΔPQR.

The area of ΔXYZ is 144 sq. cm.

The area of ΔPQR is 64 sq. cm.

The longest side of the ΔXYZ, let XY = 36 cm

According to the rule of similar triangles, 'the ratio of the area of two similar triangles is equal to the ratio of the square of any pair of the corresponding sides'.

Let the longest of ΔPQR be PQ.

Applying the rule,

$\dfrac{Area ~of ~\triangle PQR}{Area~ of ~\triangle XYZ} =\dfrac{ PQ^{2} }{ XY^{2} }$

$\implies \dfrac{64}{144} =\dfrac{ PQ^{2} }{(36)^{2} }$

$\implies \dfrac{8^{2} }{(12)^{2} } =\dfrac{ PQ^{2} }{(36)^{2} }$

Taking root on both sides,

$\implies \dfrac{8 }{12 } =\dfrac{ PQ }{36 }$

$\implies PQ= \dfrac{8\times 36 }{12 } =8\times 3=24cm$

Therefore, the length of the longest side of the  ΔPQR is 24cm.