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](https://tex.z-dn.net/?f=a%5E2%20%2Bb%5E2%20%3D%20c%5E2)
Where
a and b are the sides
c is the hypotenuse
Now substituting the values
![(4.5)^2 + b^2 = (7.5)^2](https://tex.z-dn.net/?f=%284.5%29%5E2%20%2B%20b%5E2%20%3D%20%287.5%29%5E2)
![20.25 + b^2 = 56.25](https://tex.z-dn.net/?f=20.25%20%2B%20b%5E2%20%3D%2056.25)
![b^2 = 56.25 - 20.25](https://tex.z-dn.net/?f=b%5E2%20%3D%2056.25%20-%2020.25)
![b^2 = 36](https://tex.z-dn.net/?f=b%5E2%20%3D%2036)
![b = \sqrt{36}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B36%7D)
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