Question

If ΔABC ~ ΔQRP (ar(ΔABC))/(ar(ΔPQR))=9/4,AB=18cm and BC=15cm, then find the length of PR.

Answer 1

Given :

Area of ∆ ABCArea of ∆QRP = 94


AB = 18 cm , BC = 15 cm So PR = ?

We know when two triangles are similar then " The areas of two similar triangles are proportional to the squares of their corresponding sides.

Area of ∆ ABCArea of ∆ QRP = AB2QR2 = BC2PR2 = AC2QP2
So , we take
Area of ∆ ABCArea of ∆ QRP = BC2PR2

Now substitute all given values and get

94 = 152PR2

Taking square root on both hand side , we get

32 = 15PR

PR = 10 cm

Answer 2

Solution:

Given:

• ΔABC ~ ΔQRP.
• ar (ΔABC) / ar (ΔQRP) =9/4
• AB = 18 cm and BC = 15 cm

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

➨ar (ΔABC) / ar (ΔQRP) = BC²/RP²

➨9/4 = (15)²/RP²

➨RP2 = (4/9) ×225

➨PR2 = 100

Therefore,

PR = 10 cm

Hope it will be helpful :)