. The hypotenuse of a right angled triangle is 25cm and its perimeter 56cm. Find the
length of the smallest side.
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The length of the smallest side is 7cm
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Sum of 2 sides + hypotenuse = 56
sum of 2 sides = 56-25
Sum of 2 sides = 31 cm
Let 1 side of triangle be x
Other side = (31-x)cm
By pythagorus theorum,
AC² = AB² + BC²
25² = x² + (31-x)²
625 = x² + 961 + x² - 62x
2x² - 62x + 961 - 625
2x² - 62x + 336
x² - 31x + 168
x² -24x - 7x +168
x(x-24) -7 (x-24)
(x-7)(x-24)
x = 7 or x = 24
Length of smallest side is 7cm
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