Question

Area of the triangle XYZ=60 square cm. L & M are the midpoints of the sides XY & YZ. what is the area of the portion LXZM?​

Answer 1

Answer:

Given:

In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively.

LR : RM = 1 : 2 and

LR = 3 cm

Formula:

If ΔABC ∼ ΔPQR, then

AB/PQ= BC/QR = AC/PR

Calculation:

LR : RM = x : 2x

LR = 3 cm, then

x = 3 cm

Hence, 2x = 3 × 2 = 6 cm

LM = LR + RM

⇒ LM = 3 + 6 = 9 cm

In ΔXYZ and in ΔXLM

∠X = ∠X [common]

∠XYZ = ∠XLM

∠XZY = ∠XML

∴ ΔXYZ ∼ ΔXLM

Now,

LM/YZ = XL/XY

⇒ 9/YZ = XL/2XL [∵ L is mid point of XY]

⇒ 9/YZ = 1/2

⇒ YZ = 9 × 2

∴ YZ = 18 cm

Answer 2

Answer:

| In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively, R is a point on the segment LM, such that LR : RM = 1 : 2, If LR = 3 cm, then YZ is equal to:

A. 19 cm

B. 17 cm

C. 18 cm

D. 16 cm

Step-by-step explanation:

ç is correct answer