# Math

posted by .

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?

• Math -

Let the lengths of the legs be a, b and c in increasing order. c is the hypotenuse.

b = a + 5
c = a + 10
c^2 = a^2 + b^2
Three equations in three unknowns. See what you can do with that.

c^2 = a^2 + a^2 + 10a + 25
= 2a^2 + 10a + 25
c^2 = a^2 + 20a + 100

Set the two last equations for c^2 equal to each other and solve for a.

a^2 -10a -75 = 0
(a-15)(a+5) = 0
Only the positive root is allowed.
a = 15
b = 20
c = 25

## Similar Questions

1. ### Algebra

The hypotenuse of a right triangle is 5cm long. One leg is 3cm longer than the other leg. Find the dimensions of the shorter leg. (give your answer in radical form)

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 …
3. ### math

did i do this right? The hypotenuse of a 30 ¨C 60-90 right triangle measure 18cm. What are the lengths of the longer leg and shorter leg?
4. ### Math

The shorter leg of a right triangle is 14 feet shorter than the longer leg. The hypotenuse is 26 feet. How long is each leg?
5. ### Algebra

A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30 meters longer than the length of the longer leg. How long is the longer leg?
6. ### math

The hypotenuse of a right triangle is 1 cm more than twice the shorter leg, and the longer leg is 9 cm less than three times the shorter leg. Find the lengths of the three sides of the triangle..
7. ### math

The longer leg of a right triangle is 3 more than the shorter leg. The Hypotenuse is 6 more than the shorter leg. If the perimeter of the triangle is 36, find the length of each side of the right triangle. [ Only an algebraic solution …
8. ### algebra

A garden has the shape of a right triangle with one leg 8 meters longer than the other. The hypotenuse is 8 meters less than twice the length of the shorter leg. What is the length of the shorter​ leg?
9. ### Math

The length of the hypotenuse of a right triangle is 2m more than the longer leg. The longer leg is 7m longer than the shorter leg. Find the perimeter of the triangle. ( please explain as you go)
10. ### algebra

Please show solution to this problem. In triangle A, the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer leg. Find the lengths of each side of this right triangle. Show all calculations. Short …

More Similar Questions