To find the length of the diagonal AB:
You would first use on the bottom of the box rectangle to find the diagonal CB =
Then use CB as of the triangle ACB, with AB being .
AB is approximately =
Word Bank:
5 cmthe perimeter formula for a rectangle13 cm3 cm89 cm73 cmsquare root 7 cmthe Pythagorean Theoremthe area formula for a rectangle11 cmthe hypotenusea leg
To find the length of the diagonal AB, we will use the Pythagorean Theorem. The Pythagorean Theorem states that in a right 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.
First, let's find the length of the diagonal CB. We are given the dimensions of the bottom of the box rectangle, but it's not clear which dimension is which. However, we can calculate the perimeter of the rectangle and compare it to the given word bank options to determine the correct length.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. Let's try each option from the word bank:
a) 5 cm + 13 cm + 3 cm + 11 cm = 32 cm
b) 5 cm + 13 cm + 3 cm + 89 cm ≠ 73 cm
c) 5 cm + 13 cm + 3 cm + √7 cm ≠ 73 cm
d) 5 cm + 13 cm + 3 cm + the hypotenuse ≠ 73 cm
Since option b, c, and d don't match the given perimeter of 73 cm, the correct length for CB is 32 cm.
Now, we have a right triangle ACB, with CB as one of the legs and AB as the hypotenuse. We can use the Pythagorean Theorem to find the length of AB.
The Pythagorean Theorem states that the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the other two sides (AC and CB). So, we have:
AB^2 = AC^2 + CB^2
AB^2 = AC^2 + (32 cm)^2
Unfortunately, we don't have the length of side AC, so we can't directly solve for AB. It appears that some information is missing from the given problem.