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A certain right angled triangle has its area numerically equal to its perimeter. The length of its each side is an even integer. What is the perimeter?

A certain right angled triangle has its area numerically equal to its perimeter. The length of its each side is an even integer. What is the perimeter?

Grade:10

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
Since the triangle is given to be a right angled triangle, hence we have the sides of the triangle in the ratio 3:4:5.
Now, it is given that the lengths of the sides of the triangle are even integers.
Hence we may assume the sides to be 6, 8 and 10.
(You may also attempt to solve for the sides using the given condition that area = perimeter i.e. ½ b. p = b + p + √b2 + p2
i.e. ½ .3x . 4x = 3x + 4x + √3x2 +4x2
solving this we get, x = 2)
Now, the sides are 6, 8 and 10.
So, perimeter = 6 + 8+ 10 = 24.
Area = ½ .6.8 = 24.
Hence. the required perimeter is 24.

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