Question

Ratio of the area of ∆WXY to the area of ∆WZY is 3 : 4 (see figure). If the area of ∆WXZ is 56 cm² and WY = 8 cm, find the lengths of XY and YZ.

Answer 1

Given, area of ∆WXZ = 56 cm²

⇒ `1/2` × WY × XZ = 56  ...[∵ area of triangle = `1/2` × base × height]

⇒ `1/2` × 8 × XZ = 56  ...[∵ WY = 8 cm, given]

⇒ XZ = 14 cm

∴ Area of ∆WXY : Area of ∆WZY = 3 : 4

⇒ `"Area of ∆WXY"/"Area of ∆WZY" = 3/4`

⇒ `(1/2 xx WY xx XY)/(1/2 xx YZ xx WY) = 3/4`

⇒ `(XY)/(YZ) = 3/4`

⇒ `(XY)/(XZ - XY) = 3/4`  ...[∵ YZ = XZ – XY]

⇒ `(XY)/(14 - XY) = 3/4`  ...[By cross-multiplication]

⇒ 4XY = 42 – 3XY

⇒ 7XY = 42

⇒ XY = 6 cm

So, YZ = XZ – XY = 14 – 6

YZ = 8 cm

Hence, XY = 6 cm and YZ = 8 cm.