Answer:
d) A foundation may be a rectangle : 24² + 32² = 40²
Explanation:
P.S - The exact question is -
Given - A builder set up a wooden frame in which to pour concrete for a foundation to a house. The length of the wooden frame is 24 feet. The width is 32 feet. The diagonal is 40 feet.
To find - Which best describes the foundation?
a) A foundation can not be a rectangle : 24 + 32 ≠ 40
b) A foundation can not be a rectangle : (24 + 32)² ≠ 40²
c) A foundation can not be a rectangle : √24² + 32² ≠ 40²
d) A foundation may be a rectangle : 24² + 32² = 40²
Proof -
We have to check whether the shape of the frame is rectangle or not.
As we know that,
A diagonal divides the rectangle in two right angle triangles
So,
Given that Length = 24
Width = 32
Diagonal = 40
By applying Pythagoras theorem, we get
40² = 24² + 32²
So,
The correct option is - d) A foundation may be a rectangle : 24² + 32² = 40²