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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.
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Solution
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.
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