Question

John is building a custom wall for a kitchen remodel. He knows the space for the wall is square with an area of 121 feet. How long does his diagonal brace need to be?

Answer 1

His diagonal brace need to be 15.55 feet long in the kitchen.

Explanation:

Given : The wall of the kitchen is in the shape of a square.

Area of the wall = 121 sq ft

Let us assume the each side of wall = a ft

Now, AREA OF THE SQUARE = Side x Side

⇒ a x a = 121 sq units

`\implies a ^2 = 121\\\implies a = 11`

So, each side of the kitchen wall is 11 ft.

Now,as we know in a square : EACH ANGLE IN THE SQUIRE IS A RIGHT ANGLE.

So, by Pythagoras Theorem, Diagonal D is:

`D^2 = a^2 + a^2\\\implies D^2 = 11^2 + 11^2 = 121 + 121\\\implies D^2 = 242\\\implies D = 15.55`

Hence, his diagonal brace need to be 15.55 ft long in the kitchen.