Question

The longest side of a right triangle is 39 m in length. One of the other sides is 21 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

Question 15, 5.5.61 >

Answer 1

The lengths of the two shorter sides of the triangle are 15 m and 36 m.

Step-by-step explanation:

Let's denote the shortest side of the triangle as x.

According to the problem, one side is 21 m longer than the shortest side, which means the second side is x + 21.

Using the Pythagorean theorem, we can find the length of the longest side:

39^2 = x^2 + (x + 21)^2

Simplifying this equation gives us:

1521 = 2x^2 + 42x + 441

2x^2 + 42x - 1080 = 0

Using the quadratic formula, we can solve for x:

x = (-42 ± sqrt(42^2 - 4*2*(-1080)))/(2*2)

x = (-42 ± sqrt(1764 + 8640))/4

x = (-42 ± sqrt(10404))/4

x = (-42 ± 102)/4

We take the positive value for x (since the length cannot be negative):

x = (-42 + 102)/4

x = 60/4

x = 15

Therefore, the shortest side of the triangle is 15 m long and the other side is 15 + 21 = 36 m long.