The longer leg of a right triangle is 3 ft longer than three times the shorter leg. The hypotenuse is 3 ft shorter than four times the shorter leg. Find the lengths of the three sides of the right triangle. (Please provide steps/explanation to solve this problem.)

1. 👍
2. 👎
3. 👁
1. shoter leg = x
longer leg = 3x+3
hypot= 4x-3

to solve for hypotenuse you use
a^2 + b^2 = c^2, so

(x)^2 + (3x+3)^2 = (4x-3)^2

(x)(x) + (3x+3)(3x+3) = (4x-3)(4x-3)
then multiply

(x^2) + (9x^2+18x+9) = (16x^2-24x+9)

then combine like terms

10x^2 + 18x + 9 = 16x^2 - 24x + 9

then i subtracted 10x^2 from both sides
and got:

18x + 9 = 6x^2 - 24x +9

next, i subtracted 18x from both sides:

9 = 6x^2 - 42x + 9

and then subtracted 9 from both sides

0 = 6x^2 - 42x

then pull out a 6x on the right side of the equation

0 = 6x(x-7)

so
6x=0
and
x-7=0

so x= 0 and 7

so the shorter leg is :
0 units or 7 units

the longer leg is :
3 units or 24 units

and the hypotenuse is :
-3 units or 25

and since you cant have a hypotenuse with a negative value
i think the three lengths of your triangle are

7, 24, and 25

1. 👍
2. 👎
2. Thanks for the help. :)

1. 👍
2. 👎

## Similar Questions

1. ### math

The hypotenuse of a right triangle measures 10m. One leg of the triangle is 2m longer then the other. Find the lengths of the legs. How would you solve this equation?

2. ### math/geometry

complete the statements: To find the length of the hypotenuse of a 45-45-90 triangle, multiply the length of one of the legs by:? Could the answer be .5??? to find the length of the shorter leg of a 30-60-90 triangle, multiply the

3. ### Math

A wire 32 cm long is cut into two pieces. The longer piece is 6 cm longer than the shorter piece. What is the length of the shorter piece?

4. ### math

The shorter leg of a 30°–60°–90° triangle is 10. What are the lengths of the longer leg and the hypotenuse, to the nearest tenth?

1. ### Math

1) The hypotenuse of an isosceles right triangle is 8 cm longer than either of its legs. Note that an isosceles right triangle is a right triangle whose legs are the same length. Find the exact length of its legs and its

2. ### Math

Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the largest triangle is 8 centimeters. What is the number of centimeters in the length of the

3. ### Math

Jeremy loves right triangles that have side length 1. In fact, he loves to combine them so that the hypotenuse of one becomes the leg of the next. If the longer leg of the first triangle is sqrt 11, what will be the hypotenuse of

4. ### Algebra

A wire 20 cm long is cut into two pieces. The longer piece is 4 cm longer than the shorter piece. Find the length of the shorter piece of wire

1. ### Trigonometry

The hypotenuse of a right triangle is 34cm. find the length of the two legs, if one leg is 14cm longer than the other.

2. ### Geometry

The shorter leg of a 30 degree - 60 degree - 90 degree triangle is 10. What are the lengths of the longer leg and the hypotenuse, to the nearest tenth. I do not understand these triangles can anyone help??

3. ### Math

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 5cm more than the shorter leg and the hypotenuse 10 cm more than the shorter leg. How long should the sides of the triangles be?

4. ### algebra

PLEASE HELP ASAP ? The hypotenuse of a right triangle is 5 ft long. The shorter leg is 1 ft shorter than the longer leg. Find the side lengths of the triangle. Length of the shorter leg: Length of the longer leg: Length of the