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Question
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
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Solution
Let hypotenuse=h, and other sides by x and y (x bigger than y). As per the question,
h= 2y + 1, x = y + 7 .... (i)
For right angled triangle, x2 + y2 = h2 ... (ii)
Putitng (i) in (ii), we get:
(y+ 7)2 + y2 = (2y+1)2
⇒ y2 + 49 + 14y + y2 = 4y2 +1 + 4y
⇒ 2y2 -10 y - 48 = 0
⇒ y2 - 5y - 24 = 0
⇒ y2 - 8y + 3y - 24 = 0
⇒ y (y - 8) + 3 (y - 8) = 0
⇒ (y+3) (y-8) = 0
⇒ y = 8
⇒ x=y+ 7= 15, h = 2 x 8+ 1 = 17
Hence the sides are 8, 15, 17 cm.
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