The diagonal of the floor of a rectangular closet is 15/2 feet. The sh

Question

The diagonal of the floor of a rectangular closet is 15/2 feet. The shorter side of the closet is 9/2 feet. What is the area of the closet in square feet?

(A) 37

(B) 27

(C) 54/4

(D) 21/4

(E) 5

pushpitkc · Answer

In a rectangle,  Diagonal^2 = Side1^2 + Side2^2

\frac{225}{4} = \frac{81}{4} + Side2^2  ->  Side2^2 = \frac{144}{4} = 36  ->  Side2= \sqrt{36} = 6

Therefore, the Area of the rectangle is  6*\frac{9}{2}  =  27(Option B)

ScottTargetTestPrep · Answer

We can use the Pythagorean theorem to solve for the longer side of the closet:

(9/2)^2 + b^2 = (15/2)^2

81/4 + b^2 = 225/4

b^2 = 144/4

b^2 = 36

b = 6

So the area is 9/2 x 6 = 27.

Answer: B

generis · Answer

A rectangle is divided by its diagonal into two congruent right triangles.

Rule: If a right triangle has a leg:hypotenuse ratio of 3:5 (or 4:5, or  legs  in ratio 3:4), it is a 3-4-5 right triangle.

Common 3x-4x-5x triangles include 6-8-10 (x=2), 9-12-15 (x=3), 12-16-20 (x=4), etc.

The short leg of this right triangle in the closet is  \frac{9}{2}  feet. The hypotenuse is  \frac{15}{2}  feet.

Focus on the numerator. Without any calculation we can say the other leg must be  \frac{12}{2}  feet long. The numerator matches the 9-12-15 pattern.
Keep the same denominator. OR

(leg1)^2 + (leg2)^2 = h^2 
 \frac{9}{2}^2 + (leg2)^2 = \frac{15}{2}^2 
 (leg2)^2 = (\frac{225}{4}-\frac{81}{4}) 
 \sqrt{(leg2)^2}=\sqrt{\frac{144}{4}}=\frac{12}{2} = 6

Area   = L*W = \frac{9}{2}*6=\frac{54}{2}=27

Answer B

* The multiplier is  \frac{3}{2} . (3*\frac{3}{2})=\frac{9}{2} , and  (5*\frac{3}{2})=\frac{15}{2} . If you focus on the numerator and just make the second leg's denominator match the denominator of the other two lengths, you do not need to find the multiplier or use the Pythagorean theorem.

Salamander911 · Answer

Hey Bunuel is the qustion asking to calculate the area of the closet or the rectangular floor?

Bunuel · Answer

I think the solutions above answer your question.

bumpbot · Answer

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The diagonal of the floor of a rectangular closet is 15/2 feet. The sh

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