# Hypotenuse of a right angled triangle is 2 less than 3 times its shortest side. If the remaining side is 2 more than twice the shortest side, find the area of the triangle.

Let length of shortest side(base) be x.

hypotenuse = 3x – 2.

remaining side(perpendicular) = 2x + 2 Now, According to Pythagoras theorem,

Hypotenuse2 = Base2 + Perpendicular2

(3x – 2)2 = x2 + (2x + 2)2

9x2 + 4 – 12x = x2 + 4x2 + 4 + 8x

4x2 – 20x = 0

Dividing the whole equation by 4, we get –

x2 – 5x = 0

x(x – 5) = 0

x = 0 or x – 5 = 0

But side cannot be zero

x(Base) = 5

Perpendicular = 2x + 2

= 2(5) + 2

= 12

hypotenuse = 3x – 2

= 3(5) – 2

= 13

Now, area of right triangle –  = 30 sq. unit.

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