solve the problem please.....

Picture this as a right triangle. The "distance from the wall" (i.e. the ground) is the bottom of the triangle, and the ladder is the hypotenuse. You are given the height as 6 ft, so this is the third side of the triangle.

Let **x** equal the ground / base of the triangle.

Because this is a right triangle, we can use the Pythagorean theorem (a^{2} + b^{2} = c^{2}), where **a** and **b** are the two sides making the right angle, and **c** is the hypotenuse.

We are given in the problem that **x** is two feet more than the ladder / hypotenuse. So c = x+2. One side of triangle can be **a**, and the other **b**. Let's say that **a** is the height, which is given
as 6, and **b** is the ground, which we are calling **x:**

**
**a=6 b=x c=x+2

Plug this into the Pythagorean theorem: 6^{2} + x^{2} = (x+2)^{2}

First, simplify the right side by expanding it:

(x+2)^{2} = (x+2)(x+2) = x^{2} + 4x + 4

6^{2} + x^{2} = 36 + x^{2} = x^{2} + 4x + 4

Subtract 4 from both sides: 32 + x^{2} = x^{2} + 4x

Subtract x^{2} from both sides: 32 = 4x

Divide both sides by 4: 8 = x

Remember that **x** was equal to the distance from the wall, and the length of the ladder is two feet more than **x**.

Therefore, the length of the ladder = x+2 = 8+2 = 10 feet.

## Comments

Pythagorean triples are great if you understand their application. For someone that is unfamiliar with the concept, it might be confusing