Question

Shelly is making a custom border for a quilt as shown. What length does she need to

make d, the diagonal, in feet, to ensure that she has a right angle? Round your answer
to the nearest tenth.
3 ft
5 ft
d =
ft.

Answer 1

To calculate the length of the diagonal Shelly needs for her quilt border, we apply the Pythagorean theorem, resulting in a diagonal length of approximately 5.8 feet.

Step-by-step explanation:

The student has asked about calculating the length of the diagonal in a rectangle on a quilt project to ensure that it creates a right angle. To calculate the length of diagonal d, we use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Given the lengths of the two sides as 3 ft and 5 ft, we can write the equation for the Pythagorean theorem as:

d² = 3² + 5²

d² = 9 + 25

d² = 34

To find the length of d, we take the square root:

d = √34

d ≈ 5.8 ft

Therefore, Shelly will need to make the diagonal approximately 5.8 feet long to ensure a right angle on her custom quilt border.