Question

∆ LMN ~ ∆PQR, 9 × A (∆PQR) = 16 × A (∆LMN). If QR =20 then find MN.

Answer 1

Heya !!!

Given that ∆LMN and ∆PQR similar triangles.

9 × Area ( ∆PQR) = 16 × Area(∆LMN)

Area of ∆LMN : Area of ∆PQR = 9:16

We know that,

Area of two similar triangles is always Equal to square of their corresponding sides.

Therefore,

Area ( ∆LMN) / Area ( ∆PQR) = (MN/QR)²

9/16 = (MN)² / (20)²

9/16 = (MN)² / 400

(MN)² = 9×400/16


(MN) = ✓9×400/16


MN = 3×20/4



MN = 3 × 5 = 15 cm

HOPE IT WILL HELP YOU....... :-)

Answer 2

Answer:

Step-by-step explanation:

Given that ∆LMN and ∆PQR similar triangles.

9 × Area ( ∆PQR) = 16 × Area(∆LMN)

Area of ∆LMN : Area of ∆PQR = 9:16

We know that,

Area of two similar triangles is always Equal to square of their corresponding sides.

Therefore,

Area ( ∆LMN) / Area ( ∆PQR) = (MN/QR)²

9/16 = (MN)² / (20)²

9/16 = (MN)² / 400

(MN)² = 9×400/16

(MN) = ✓9×400/16

MN = 3×20/4

MN = 3 × 5 = 15