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प्रश्न
The hypotenuse of a right angled triangle is 25 cm and its perimeter 56 cm. Find the length of the smallest side
उत्तर
Perimeter of a right angle triangle = 56cm
Sum of the two sides + hypotenuse = 56
Sum of the two sides = 56 – 25
= 31 cm
Let one side of the triangle be “x”
The other side of the triangle = (31 – x)cm
By Pythagoras theorem
AB2 + BC2 = AC2
x2 + (31 – x)2 = 252
x2 + 961 + x2 – 62x = 625
2x2 – 62x + 961 – 625 = 0
2x2 – 62x + 336 = 0
⇒ x2 – 31x + 168 = 0
(x – 24) (x – 7) = 0
x – 24 = 0 (or) x – 7 = 0
x = 24 (or) x = 7
Length of the smallest side is 7 cm
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