Question

The hypotenuse of a right triangle is 2 ft less than three times the shortest leg. The longer leg is 3 ft less than three times the shorter leg. Find the length of each side of the triangle.

a) Hypotenuse: 7 ft, Shorter leg: 2 ft, Longer leg: 5 ft

b) Hypotenuse: 10 ft, Shorter leg: 3 ft, Longer leg: 7 ft

c) Hypotenuse: 5 ft, Shorter leg: 1 ft, Longer leg: 4 ft

d) Hypotenuse: 6 ft, Shorter leg: 2 ft, Longer leg: 4 ft

Answer 1

To find the length of each side of the right triangle, we can use the Pythagorean theorem and the given information about the hypotenuse and the longer leg. By setting up and solving equations, we can find that the length of the shortest leg is 5/8 ft, the longer leg is 27/8 ft, and the hypotenuse is 23/8 ft.

Step-by-step explanation:

In this problem, we are given that the hypotenuse of a right triangle is 2 ft less than three times the shortest leg, and the longer leg is 3 ft less than three times the shorter leg. Let's assume that the shortest leg is represented by 'x' ft.

According to the given information, we can write two equations:

Hypotenuse = 3x - 2

Longer Leg = 3x - 3

Using the Pythagorean theorem, we know that a² + b² = c², where 'a' and 'b' are the legs and 'c' is the hypotenuse.

Substituting the values we get:

x² + (3x - 3)² = (3x - 2)²

Simplifying the equation, we get:

x² + 9x² - 18x + 9 = 9x² - 12x + 4

After canceling out the like terms and simplifying the equation, we get:

8x = 5

Dividing by 8 on both sides, we get:

x = 5/8 ft

Therefore, the length of the shortest leg is 5/8 ft, the longer leg is (3 * (5/8) - 3) ft, and the hypotenuse is (3 * (5/8) - 2) ft.