# Algebra II

In a right triangle, the length of the longer leg is 7 more inches than the shorter leg. The length of the hypotenuse is 8 more inches than the length of the shorter leg.

A). If the shorter leg is representd by x, write expressions for the longer leg and the hypotenuse in terms of x

B). Write an equation using the Pythagoreum Theorem that relates the three sides together and solve it for the value of x. Then identify the lengths of the longer side and hypotenuse.

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. B.
(x+7)^2 + x^2 = (x+8)^2

x^2 + 14 x + 49 + x^2 = x^2 + 16 x + 64

x^2 - 2 x - 15 = 0

(x-5)(x+3) = 0
so
x = 5
x + 7 = 12
x+8 = 13

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### Geometry

Please check my answers 1. A triangle has side lengths of 34 in, 20 in, and 47 in. Is the triangle acute, obtuse or right? a. Right b. Obtuse* c. Acute 2. Quilt squares are cut on the diagonal to form triangular quilt pieces. The

2. ### 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?

3. ### 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

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

1. ### geotrig

The hypotenuse of a right triangle is 6 more than the shorter leg. The longer leg is 3 more than the shorter leg. What is the measure of the shorter leg of the right triangle?

2. ### calculus

A right triangle has legs of 24 inches and 32 inches whose sides are changing. The short leg is increasing by 8 in/sec and the long leg is shrinking at 5 in/sec. What is the rate of change of the hypotenuse?

3. ### trig

a right triangle contains a 25 angle. if me leg is of length 5 inches what is the length of the hypotenuse

4. ### math

I have 14 questions and I was wondering if someone could check my answers. This is a do or die situation. If I don't get an A, I may not get to graduate. I really appreciate you taking your time to double check theses for me.

1. ### 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

2. ### 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.

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. ### Math

PLEASE HELP I REALLY NEED IT!! A rectangular box is 8 inches in length, 3 inches in width, and 5 inches in height. The figure shows a rectangular box of length 8 inches, width 3 inches, and height 5 inches. The diagonal of this