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If the perimeter of a rectangular property is 46 meters

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If the perimeter of a rectangular property is 46 meters

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If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 square meters, what is the length of each of the shorter sides?

A. 4
B. 6
C. 9
D. 18
E. 23

The OA is the option A.

Experts, what are the equations I should use? Are 2X+2Y=46 and X*Y=76? I'd be thankful for your help.

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Hello vjesus12.

Let's take a look at your question.

You are correct, you have to use the formulas $$2X+2Y=46\ \ and\ \ \ \ \ X\cdot Y=76 .$$ Hence, $$X+Y=23\ \ and\ \ \ \ \ X=\frac{76}{Y}.$$ Replacing X on the first equation we get $$\frac{76}{Y}+Y=23\ \Leftrightarrow\ \ \ 76+Y^2=23Y\ \Leftrightarrow\ \ Y^2-23Y+76=0$$ $$Y^2-23Y+76=0\ \Leftrightarrow\ \ \left(Y-4\right)\left(Y-19\right)=0.$$ Hence, Y=4 or Y=19.

If Y=4 then X+Y=23 implies that X=23-4=19. In this case, the dimensions of the rectangle are 4 and 19.

If Y=19 then X+Y=23 implies that X=23-19=4. In this case, the dimensions of the rectangle are 4 and 19.

In each case, the length of the shorter side is equal to 4.

This is why the correct answer is the option A.

I hope this answer can help you.

Feel free to ask me again if you have a doubt.

Regards.

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VJesus12 wrote:
If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 square meters, what is the length of each of the shorter sides?

A. 4
B. 6
C. 9
D. 18
E. 23
In any rectangle:
A = LW.
P = 2L + 2W.

We can PLUG IN THE ANSWERS, which represent the value of W.
Since LW = 76, the correct answer is almost certainly a factor of 76.
Of the five answer choices, only A divides evenly into 76.
When the correct answer is plugged in, P = 46.

A: W=4
Since LW = 76, we get:
(L)(4) = 76
L = 19.
P = 2L + 2W = 2(19) + 2(4) = 38 + 8 = 46.
Success!

The correct answer is A.

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VJesus12 wrote:
If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 square meters, what is the length of each of the shorter sides?

A. 4
B. 6
C. 9
D. 18
E. 23
We can let W = the width and L = the length and create the equations:

2W + 2L = 46

W + L = 23

L = 23 - W

and

WL = 76

Substituting, we have:

W(23 - W) = 76

23W - W^2 = 76

-W^2 + 23W - 76 = 0

W^2 - 23W + 76 = 0

(W - 4)(W - 19) = 0

W = 4 or W = 19

If W = 4, then L = 23 - 4 = 19.

If W = 19, then L = 23 - 19 = 4.

We see that the length of each of the shorter sides is 4.

Answer:A

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Founder and CEO
scott@targettestprep.com



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