Question

The perimeter of the right angled triangle is five times the length of its shortest side.The numerical value of the shortest side. Find the lengths of the three sides of the triangle​

Answer 1

Answer:

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.

Step-by-step explanation: