Aptitude - Area - Discussion

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.

Using the formula given hy^2=base^2+hgt^2.

We get the ans as 6ft and here in the question we have to find the area in square feet so we have to multiply with 4.5 = 9/2 so we have the ans of 27 with the product of 4.5 and 6 because we are considering the side but not the diagonal.

Using the formula given hy^2=base^2+hgt^2.

We get the ans as 6ft and here in the question we have to find the area in square feet so we have to multiply with 4.5 = 9/2 so we have the ans of 27 with the product of 4.5 and 6 because we are considering the side but not the diagonal.

(Hypotenuse)2 = (Base)2 + (Height)2.

So! H^2 = hy^2 - Base^2 ----- eq1.
Here hy = 15/2 , base= 9/2 ...................(*9/2 = 4.5).

After solve eq1, we get 6ft

Area of closet = 6ft * 4.5 ft (this come from base, see to * ..).

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.

@Siddhesh.

In the question itself one of the side value is given that is 4*1^2 (shortest closet). Since it s shortest closet we are taking that as breadth value 4.5 feet and derived value as the length (6 feet).

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.

Length of closet will come 12/2 feet. (Using Pythagoras theory).

And area = l*b = (9/2)*(12/2) = 9*3 = 36 sq.feet.

Then how it comes 27 sq.feet?

@Siddhesh.

Breadth i.e. the smallest side is 9/2 ie 4.5 since the area of rectangle is length*breadth therefore the final step is 6*9/2 or 6*4.5

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