Question

The perimeter of a right angled triangle is five times the length of its shortest side.

The numerical value of the area of the triangle is 15 times the numerical value of the

length of the shortest side . Find the lengths of the three sides of the triangle.

please ans fast

Answer 1

Let the sides of the triangle are x(shorter side), y,z(hypotenuse).

We know that z^2 = x^2 + y^2  ----- (1)

Given that perimeter of a right-angled triangle is 5 times the length of its shortest side.

= > x + y + z = 5x  ----- (2)


Given that Area of a triangle is 15 times the numerical value of the length of the shortest side.

= > 1/2 * x * y = 15 * x

= > xy = 30x

= > y = 30.  ----- (3) 

Substitute (3) in (2), we get

= > x + 30 + z = 5x

= > z = 4x - 30  ------ (4)

Substitute (4) in (1), we get

= > (4x - 30)^2 = x^2 + (30)^2

= > 16x^2 + 900 - 240x = x^2 + 900

= > 15x^2 - 240x = 0

= > 15x(x - 16) = 0

= > x - 16 = 0

= > x = 16.

Substitute x = 16 in (1), we get

= > z^2 = 16^2 + 30^2

= > z^2 = 256 + 900

= > z^2 = 1156

= > z = 34.



Therefore the lengths of the three sides of the triangle are 16, 30, 34.



Hope this helps!

Answer 2

I have solved it on my own......

HOPE IT WILL BE HELPFUL FOR YOU.............