Exercise 19 Page 610

Lucia makes a triangular garden in one corner of her fenced rectangular backyard. We know that one of the fenced sides of the garden is $15$ feet, and that she has $25$ feet of edging to use along the unfenced side of the garden.

Since the triangular garden is in the corner of a rectangle, it is a right triangle. Therefore, we will use the Pythagorean Theorem to determine the length $\ell$ of the other fenced side. Let's recall the theorem.

Pythagorean Theorem

If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

In our case the lengths of the legs are $15$ feet and $\ell$ feet, and the length of the hypotenuse is $25$ feet. Finally we will solve the obtained equation for the length $\ell$ of the other leg. Please note that we only consider the positive root of the equation, since $\ell$ represents the length of the leg. We have that the other fenced side of the garden is $20$ feet long.