Exercise 34 Page 645

Let's begin with recalling the 45^(∘)-45^(∘)-90^(∘) Triangle Theorem. This theorem tells us that in an isosceles right triangle the legs l are congruent and the length of the hypotenuse is sqrt(2) times the length of a leg.

Now, let's take a look at the given picture. We are given that the quilt block is made up of a square and four isosceles right triangles. Notice that x is the leg length of each of the inner triangles.

According to the theorem we recalled at the beginning, the length of the hypotenuse in a right isosceles triangle is sqrt(2) times the length of a leg. Using this information, we can write an equation. xsqrt(2)=6sqrt(2) ⇓ x=6 The value of x is 6 inches. Next we are asked to determine the side length of the entire quilt block. Let s represents this measure.

As we can see, the side length of the entire quilt block is two times the length of the leg of an inner triangle. s= 2* 6=12 The side length of the entire quilt block is 12 inches.