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Question
The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.
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Solution
Let hypotenuse=h, and other sides by x and y (x bigger than y). As per the question,
h = 17 , X2 + y2 = 17 X 17
⇒ x2 + y2 = 289 ..... (i)
In second scenario, sides become Sy and 2x, new h becomes 50 cm
⇒ (5y)2 + (2x)2 = 50 x 50
⇒ 25y2 + 4x2= 2500
⇒ (21y2 + 4 y2 )+ 4x2 = 2500 ..... (ii)
Putitng (i) in (ii), we get:
21y2 + 4(289) = 2500
⇒ 21y2= 1344
⇒ y2 = 64
Hence y = 8cm.
Putting this is (i), we get
⇒ x2= 289 - 64 = 225
⇒ x= 25cm
Hence, the sides are 8, 15, 17 cm.
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