Posted by **Bethany** on Tuesday, February 8, 2011 at 12:47am.

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 -
**drwls**, Tuesday, February 8, 2011 at 1:31am
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

## Answer This Question

## Related Questions

- math - The longer leg of a right triangle is 3 more than the shorter leg. The ...
- math - The hypotenuse of a right triangle is 1 cm more than twice the shorter ...
- Math - The length of the hypotenuse of a right triangle is 2m more than the ...
- math - did i do this right? The hypotenuse of a 30 ¨C 60-90 right triangle ...
- Quadratic Equations - The longer leg of a right triangle is 3 ft longer than ...
- algebra - A garden has the shape of a right triangle with one leg 8 meters ...
- Algebra - The hypotenuse of a right triangle is 5cm long. One leg is 3cm longer ...
- Algebra - the length of the longer leg of a right triangle is 13 ft more than 3 ...
- Algebra - A lot is in the shape of a right triangle. The shorter leg measures 90...
- math - the shorter leg of a right triangle is 9 inches shorter than the longer ...

More Related Questions