Question

Will mark brainliest, please answer:)

Fiona decides to use the design of the box that is 2 feet high by 6 feet wide by 8 feet long. She wants to reinforce the bottom of the box with diagonal pieces of wood from corner to the opposite corner. How long should she cut the diagonal piece of wood. Explain.

Answer 1

Answer:

She should cut each diagonal piece 10 ft long.

Step-by-step explanation:

The bottom face of the box is a rectangle 8 ft by 6 ft.

A diagonal of a rectangle divides the rectangle into two congruent right triangles. With a right triangle you can use the Pythagorean theorem.

a = length of rectangle = leg of right triangle

b = width of rectangle = other leg of right triangle

c = diagonal of rectangle = hypotenuse of right triangle

a^2 + b^2 = c^2

(8 ft)^2 + (6 ft)^2 = c^2

64 ft^2 + 36 ft^2 = c^2

c^2 = 100 ft^2

Take the square root of each side.

c = 10 ft

Answer: She should cut each diagonal piece 10 ft long.

Answer 2

Answer:

The diagonal piece of wood should be 10 feet long.

Step-by-step explanation:

The diagonal piece of wood will form a right-angled triangle with the width and length  of the box. By the Pythagoras Theorem:

x^2 = 6^2 + 8^2   where x is the  length of the diagonal.

x^2 = 36 + 64

x^2 = 100

x = 10 feet.