Question

A small shelf it's on two braces that are in the shape of a right triangle. The brace attached to the wall is 4.5 inches and the hypotenuse is 7.5 inches. The brace holding the shelf is the same length as the width of the shelf. What is the width of the shelf?

Answer 1

Answer:

The width of the shelf is 6 inches

Step-by-step explanation:

Given:

Length of the brace attached to the wall  = 4.5 inches

The Length of the hypotenuse = 7.5 inches

To Find:

The width of the shelf =?

Solution:

The brace holding the shelf is in the shape of the right triangle

Where one side is of length 4.5 inches and Hypotenuse of length is 7.5 inches

In a Right triangle according to the Pythagorean theorem

$a^2 +b^2 = c^2$

Where

a and b are the sides

c is the hypotenuse

Now substituting the values

$(4.5)^2 + b^2 = (7.5)^2$

$20.25 + b^2 = 56.25$

$b^2 = 56.25 - 20.25$

$b^2 = 36$

$b = \sqrt{36}$

b = 6

This side of the brace is same as the width of the shelf, so the width of the shelf is also 6 inches