Question

In right angled triangle, the sides forming right angle differ by 7cm. find its side if it's perimeter is 40 cm
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Answer 1

The sides of a right angled triangle are: 8, 15, 17 or 65, 72, 97 if it's perimeter is 40 cm.

Perimeter of right angled triangle

P = a + b + √ (a^2 + b^2)

where, a and b are the sides of a rt. angled triangle other than hypotenuse.

a - b = 7 cm (given)

⇒ a = 7 + b

P = 40 cm (given)

∴ 40 = a + b + √ (a^2 + b^2)

⇒ 40 = 7 + b + b + √ ((7+b)^2 + b^2)

40 - 7 = 2b + √ ((7+b)^2 + b^2)

33 - 2b = √ ((7+b)^2 + b^2)

squaring on both sides, we get,

(33 - 2b)^2 = (7+b)^2 + b^2

33^2 + 4b^2 - 132b = 7^2 + b^2 + 14b + b^2

2b^2 - 146b + 1040 = 0

b = 8, 65

a = 7 + b

a = 15, 72

c = √ (a^2 + b^2)

c = 17, 97

Thus the sides of a right angled triangle are: 8, 15, 17 or 65, 72, 97.