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

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Math Expert
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The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

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13 Feb 2018, 05:53
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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

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The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

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13 Feb 2018, 07:04
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Bunuel wrote:
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

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)
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Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

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14 Feb 2018, 10:57
Bunuel wrote:
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

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.

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The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

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26 Feb 2018, 18:37
Bunuel wrote:
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

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

*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.
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Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

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07 Mar 2018, 10:04
Hey Bunuel is the qustion asking to calculate the area of the closet or the rectangular floor?
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Posts: 55271
Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

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07 Mar 2018, 10:17
Salamander911 wrote:
Hey Bunuel is the qustion asking to calculate the area of the closet or the rectangular floor?

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Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

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16 Mar 2019, 19:40
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Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh   [#permalink] 16 Mar 2019, 19:40
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