Question

The side of a right -angle triangle containing the right angle are 5x and ( 3x-1) cm. If the area of the triangle be 60cm square, calculate the length of the side of the triangle.

Answer 1

Hey friend, Here is your answer-

Let the triangle be ABC.

Then AB = 5x and BC = (3x-1)

Area of triangle = 1/2 × b × h

60 = 1/2 × 5x × (3x - 1)

120 = 15x^2 - 5x

15x^2 - 5x - 120 = 0
3x^2 - x - 24 = 0

By usingb^2 - 4ac,
= (-1)^2 - 4 × 3 × -24
= 1 - 4 × -72
= 1+ 288
= 289

x = -b +/- root b2-4ac / 2a
x = 1 + root 289 /6
or
x = 1 - root 289 / 6

x = 1 + 17 / 6
or
x = 1- 17 / 6
x = 3 or x = - 8/3

Therefore x = 3

The sides are 5x = 5×3 = 15 cm ,
3x - 1 = 3× 3 - 1 = 8 cm

Sides are 15 cm and 8 cm.

Hope it will help you.

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