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

Given:

Given:In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively. LR : RM = 1 : 2 andLR = 3 cm

Given:In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively. LR : RM = 1 : 2 andLR = 3 cmFormula:If ΔABC ∼ ΔPQR, thenAB/PQ= BC/QR = AC/PR

Given:In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively. LR : RM = 1 : 2 andLR = 3 cmFormula:If ΔABC ∼ ΔPQR, thenAB/PQ= BC/QR = AC/PRCalculation:LR : RM = x : 2xLR = 3 cm, thenx = 3 cmHence, 2x = 3 × 2 = 6 cm

Given:In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively. LR : RM = 1 : 2 andLR = 3 cmFormula:If ΔABC ∼ ΔPQR, thenAB/PQ= BC/QR = AC/PRCalculation:LR : RM = x : 2xLR = 3 cm, thenx = 3 cmHence, 2x = 3 × 2 = 6 cmLM = LR + RM⇒ LM = 3 + 6 = 9 cmIn ΔXYZ and in ΔXLM∠X = ∠X

∠XYZ = ∠XLM

∠XYZ = ∠XLM∠XZY = ∠XML

XL/XY⇒ 9/YZ = XL/2XL [ L is mid point of XY]⇒ 9/YZ = 1/2

∠XYZ = ∠XLM∠XZY = ∠XML∴ ΔXYZ ∼ ΔXLMNow,LM/YZ = XL/XY⇒ 9/YZ = XL/2XL [ L is mid point of XY]⇒ 9/YZ = 1/2⇒ YZ = 9 × 2

= 18 cm