Question

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

(a) 8 m, 15 m, 17 m
(b) 10 m, 24 m, 26 m
(c) 12 m, 35 m, 37 m
(d) 14 m, 48 m, 50 m

Answer 1

To solve this problem, we can use the Pythagorean theorem. Let's define the sides of the triangle and then solve the equation to find the lengths. The sides of the triangle are 8 m, 15 m, and 17 m. Therefore, the correct answer is (a) 8 m, 15 m, 17 m.

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem. Let's define the sides of the triangle as follows:

• Shortest side: x
• Hypotenuse: 2x + 6
• Third side: (2x + 6) - 2 = 2x + 4

According to the Pythagorean theorem, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. So, we have:

x2 + (2x + 4)2 = (2x + 6)2

Simplifying and solving this equation, we get x = 8. Substituting this value back into the expressions for the sides, we find the sides of the triangle are 8 m, 15 m, and 17 m. Therefore, the correct answer is (a) 8 m, 15 m, 17 m.