Answer:
The width of the shelf is 6 inches.
Step-by-step explanation:
The leg (brace) attached to the wall is 4.5 inches.
The length of the hypotenuse = 7.5 inches.
Also, the Length of leg holding the shelf = Width of the shelf
Now, as the brace is in the shape of right triangle.
In a Right Triangle, by PYTHAGORAS THEOREM:
[tex](Length)^2 + (Base)^2 = (Hypotenuse)^2[/tex]
Putting here the values of hypotenuse and base, we get:
[tex]L^2 + (4.5)^2 = (7.5)^2\\\implies L^2 = 56.25-20.25\\\implies L^2 = 36\\\implies L = \sqrt{36} = 6[/tex]
So, the length of the leg = 6 inches
Hence, the width of the shelf is 6 inches.
