Aptitude - Area - Discussion

Assume,
length = x.

Formula.
(diagonal)²= (length)²+ (width)².
(7.5)² = (x)² + (4.5)²
(x)² = (7.5)² - (4.5)²
(x)² = 36
x = 6.

It means the length is 6.

Area = length x width.
= 6 x 4.5.
= 27 sq. ft.

Closet only means a closed space. So here in a rectangle diagonal=7. 5 feet and breadth=4. 5 feet. So using hypotenuse2=base2+altitude2 we can easily find the lenght. So area= l*b.

Please explain the closest feet.

area=1/2 (d^2),
= 225/8,
= 28.

A closet is a little room where clothes are hung. This closet is in the shape of a rectangle. The diagonal of the floor of the closet is 7.5 ft and the shorter side is 4.5 ft. To find the area of the floor we need the measure of the longer side. Remember that when we have a diagonal in a rectangle or square we will have 2 triangles.

Now using the Pythagoras Theorem:

a^2 + b^2 = c^2.
4.5^2 +b^2 =7.5^2.
b^2 = 7.5^2 - 4.5^2.
b^2 = 56.25^2 - 20.25^2.
b^2 = 36.

Therefore b = 6 (length of longer side).

Area = length x width.
= 6 x 4.5.
= 27ft^2.

Shouldn't closet mean a cuboid or a cube?

Once look at the explanation at the top, I hope you will get.

How 6 is coming? Can you simplify?

If suitable sketches were given and hypotenuse theorem is to be applied on required statement, learners got it easy.

@Kiran Joy.

Thank You so much. Now the logic of the question is clear.