Pythagorean Theorem Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A right triangle has legs of length x+1x + 1 and x+8x + 8, and hypotenuse 1313. Find xx.

Solution

  1. 1
    Apply the Pythagorean theorem: (x+1)2+(x+8)2=132(x + 1)^2 + (x + 8)^2 = 13^2.
  2. 2
    Expand and simplify: x2+2x+1+x2+16x+64=169⇒2x2+18x−104=0x^2 + 2x + 1 + x^2 + 16x + 64 = 169 \Rightarrow 2x^2 + 18x - 104 = 0.
  3. 3
    Divide by 22: x2+9x−52=0=(x+13)(x−4)x^2 + 9x - 52 = 0 = (x + 13)(x - 4), so x=4x = 4 or x=−13x = -13.
  4. 4
    Since side lengths must be positive, x=4x = 4.

Answer

x=4x = 4
The Pythagorean theorem can generate algebra equations when side lengths are written with variables. After solving, reject any answer that would make a side length negative.

About Pythagorean Theorem

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Learn more about Pythagorean Theorem →

More Pythagorean Theorem Examples

Example 1 easy

A right triangle has legs of length [formula] and [formula]. Find the hypotenuse.

Example 2 medium

A right triangle has a hypotenuse of [formula] and one leg of length [formula]. Find the other leg.

Example 3 hard

A ladder [formula] m long leans against a wall. The foot of the ladder is [formula] m from the base

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