Question

The hypotenuse of right angled triangle is 6 metres more than twice the shortest side .Of the tird side is 2 metres less than hypotenuse ,find the sidesaccelerationof the triangle

Answer 1

the hypotenuse of a right angled triangle is 6m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.

Let x = shortest side

then

2x+6 = hypotenuse

2x+6-2 = 2x+4 = long side

.

x^2 + (2x+4)^2 = (2x+6)^2

x^2 + (2x+4)(2x+4) = (2x+6)(2x+6)

x^2 + 4x^2+16x+16 = 4x^2+24x+36

5x^2+16x+16 = 4x^2+24x+36

x^2+16x+16 = 24x+36

x^2-8x+16 = 36

x^2-8x-20 = 0

(x-10)(x+2) = 0

x {-2, 10}

throw out the negative solution leaving:

x = 10m (short side)

.

hypotenuse:

2x+6 = 2(10)+6 = 20+6 = 26m

.

long side:

2x+4 = 2(10)+4 = 20+4 = 24m