The perimeter of rectangle A is 200 meters. The length of rectangle B

Question

The perimeter of rectangle A is 200 meters. The length of rectangle B is 10 meters less than the length of rectangle A and the width of rectangle B is 10 meters more than the width of rectangle A. If rectangle B is a square, what is the width, in meters, of rectangle A ?

A. 10

B. 20

C. 40

D. 50

E. 60

A. 10

B. 20

C. 40

D. 50

E. 60

Gnpth · Accepted Answer

2(L+W)=200. Then L+W=100

Now For B,

Lenght of B= L-10. And Width of B= W+10.

We are told that B is square. Then Length of B= Width of B

L-10=W+10. So L= W+20.

W+20+W=100

2W=80

W=40. So the Answer is C.

generis · Answer

For the square (rectangle B) the net change in perimeter, from decreased L (-10), twice, and (+10) in W, twice, is 0.

All sides of a square are equal. If we add 10 to two sides, and subtract 10 from two sides, 
because we started with equal side lengths, the perimeter does not change.

If rectangle-square B has side = 50.
Perimeter is 4s = 200. 
Each L increases by 10 (to make rectangle A): two lengths = 60
Each W decreases by 10 (to make rectangle A): two widths = 40
Perimeter of rectangle A? 60 + 60 + 40 + 40 = 200 (same as rectangle-square B) 
 
So the perimeter of rectangle A equals perimeter of square (rectangle B).

Perimeter of square = 4s

4s = 200
s = 50

If the side of the square (B) is 50, then the width of rectangle A is (50 - 10) = 40.

Answer C

praveen8047 · Answer

For Rectangle A, 2(l+b) = 200 or l+b = 100 -------(1) where l & b are the length and breadth of rectangle A
For Rectangle B, which is a square: l-10 = b+10 ----- (2) (as the sides of the squares are equal)
Using (1) and (2), b= 40

CyberStein · Answer

Permiter = 2(length + width)

A = 200 = 2(l +w)
B = 2((l-10) + (w +10)
given B = square, you know that B's length is equal to its width
(l-10) = (10 + w)
l = 20 + w
200 = 2((20 +w) + w)
100 = ((20 + w) + w)
80 = 2w
40 =w

Therefore the answer is (C)

ScottTargetTestPrep · Answer

We can let the width of rectangle A = W and the length of rectangle A = L and create the equations:

2L + 2W = 200

L + W = 100

We also know that the width of rectangle B is (10 + W) and its length is (L - 10). Since B is a square, we have:

10 + W = L - 10

W - L = -20

Adding the two equations, we have:

2W = 80

W = 40

Alternate solution:

Since the length of rectangle B is 10 less than the length of rectangle A but the width of B is 10 more than the width of A, we know that B and A must have equal perimeters. Therefore, the perimeter of B is 200. Since we are told that B is a square, a side of B must be 50. Since this is 10 more than the width of A, the width of A must be 40.

Answer: C

Salsanousi · Answer

Perimeter of A = 200 = 2 (L_A+W_A)

Perimeter of A = 100 = L_A+W_A

LB = L_A - 10

WB = W_A + 10

We can then substitute back in the equation so that  100 = L_B + W_B

Given that B is a square so  L_B  and  W_B  are both 50.

W_A = W_B - 10 = 50 - 10 = 40.

Answer choice C

SandeepS030489 · Answer

Let the length of rectangle A be x
Since B is square, length and width will be the same
Side of B is 10 meters less than length of A i.e. x - 10 (1)
Side of B is 10 meters more than the width of A (Means width of A is 10 less than side of B) i.e. (x - 10) - 10; x - 20 (2),
perimeter of A : 200 meters = 2*(x + x - 20); 200 = 4x - 40,
240 = 4x; x = 60,
Width is x - 20 = 60 - 20 = 40 meters
Answer Choice C

Rachit4126 · Answer

New Method on after thought

Rect A: 2(l+b)=200
l+b=100

Let Rect B: l1=l-10; b1=b+10

Still l1+b1=100- which must be 50-50 since its a square .

We simply have to reduce 10 in 50 and look for 40 in the answer choices which is option C.

Of course 60 is also one of the option but since width of B is 10 MORE than A, width of A will be 10 less than B which is 40 and not 60.

Hope it helps.

RajdeepGM · Answer

If B is a square, sides of B should be such that if we do 10 less and 10 more and than add the sum should be 100 ie half of perimtr of A. (to comply with condition of first rectangle)

Clearly only possible when its 50. So width is 50 less 10 ie 40.

Layman way!

Posted from my mobile device

MHIKER · Answer

The \ same \ amount \ (10) \ of \ decrease \ and \ increase \ in \ length \ and \ width \ will \ not \ change \ the \ perimeter.

The perimeter of the rectangle A = 200

The perimeter of rectangle B, which is a square  4s=200

s=\frac{200}{4}=50=lenght = width

As the width of the Rectangle B (square) is 10 meters more than the perimeter so the width of rectangle A is  50-10=40

The answer is C

ShahadatHJ · Answer

Let one side of B = X
Length of A = X+10
Width of A = X-10
Perimeter = 2*  = 200
X = 50
Width of A = 50-10 = 40

bumpbot · Answer

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The perimeter of rectangle A is 200 meters. The length of rectangle B

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The perimeter of rectangle A is 200 meters. The length of rectangle B

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