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505-555 (Easy)|   Geometry|      
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In a rectangle with area 572, the length of the shortest side is 4 met 06 Jun 2017, 11:38
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D
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83% (02:35) correct 17% (03:07) wrong based on 125 sessions

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In a rectangle with area 572, the length of the shortest side is 4 meters shorter than the length of the longest side. What is the perimeter of the rectangle?

A. 90
B. 92
C. 94
D. 96
E. 98
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D
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In a rectangle with area 572, the length of the shortest side is 4 met 06 Jun 2017, 11:43
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Ans :D
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In a rectangle with area 572, the length of the shortest side is 4 met 08 Jun 2017, 17:19
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Bunuel
In a rectangle with area 572, the length of the shortest side is 4 meters shorter than the length of the longest side. What is the perimeter of the rectangle?

A. 90
B. 92
C. 94
D. 96
E. 98
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\(A = l * w\)

\((w + 4) = l\)

\((w + 4)*(w) = 572\)

\(w^2 + 4w - 572 = 0\)

\((w + 26)(w - 22) = 0\)

w can't be negative, \(w = 22\)

\((w + 4) = l\)
\(l = 22+4 = 26\)

\(P = 2l + 2w\)
\(= 52 + 44\)
\(P = 96\)

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Answer D
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In a rectangle with area 572, the length of the shortest side is 4 met 08 Jun 2017, 18:46
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22*26 is 572, so Perimeter is 22+22+26+26 = 96.
Ans - D
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In a rectangle with area 572, the length of the shortest side is 4 met 08 Jun 2017, 19:50
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b=l-4
l(l-4)=572---> l=26---> b=22
Perimeter= 2(l+b)= 2(48)
Answer D: 96
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In a rectangle with area 572, the length of the shortest side is 4 met 08 Jun 2017, 20:36
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Bunuel
In a rectangle with area 572, the length of the shortest side is 4 meters shorter than the length of the longest side. What is the perimeter of the rectangle?

A. 90
B. 92
C. 94
D. 96
E. 98
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If Length = x
Width = (x-4)
Area = x*(x-4) = 572
but 22*26 = 572
hence
x = 26

perimeter = 2(x+x-4) = 4x-8 = 104-8 = 96

Answer: Option D
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In a rectangle with area 572, the length of the shortest side is 4 met 13 Jun 2017, 12:19
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Bunuel
In a rectangle with area 572, the length of the shortest side is 4 meters shorter than the length of the longest side. What is the perimeter of the rectangle?

A. 90
B. 92
C. 94
D. 96
E. 98
Show more

We can let x = the long side and y = the short side.

Since the area is 572, xy = 572.

Since the length of the shortest side is 4 meters shorter than the length of the longest side, x = y + 4.

Since x = y + 4, we can substitute y + 4 for x in the equation xy = 572:

y(y + 4) = 572

y^2 + 4y = 572

y^2 + 4y - 572 = 0

(y + 26)(y - 22) = 0

y = -26 or y = 22

Since y must be positive, y = 22.

Since y is 22, x is 26 and the perimeter is:

2(22) + 2(26) = 44 + 52 = 96

Answer: D
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In a rectangle with area 572, the length of the shortest side is 4 met 06 Aug 2022, 09:00
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I think the qs is wrong or poorly framed the longest side of the rectangle is the diagonal

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