In the adjoining figure, AC+ AB = 5AD and AC – AD = 8. Then the area of the rectangle ABCD is
Explanation:
Since AD = BC (Opposite sides of a rectangle are equal.) AB + AC = 5BC and AC – BC = 8 or AC = BC + 8 ∴ AB = 4(BC – 2) By Pythagoras’ Theorem, AB2 + BC2 = AC2 Expressing AB and AC in terms of BC we get, BC = 5. ∴ AB = 12 and AC = 13 So area of the rectangle = 5 × 12 = 60.
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