7. nine playing cards from the same
deck are placed as shown in the
figure below to form a large rectangle
of area 180 sq. in. what is the
perimeter, in inches, of this large
rectangle?
a. 29
b. 58
c. 64
d. 116

B. The perimeter of the given figure is 58 units.

Step-by-step explanation:

Here, the attachment is missing.

For the reference, i am attaching the correct figure specified in the question.

Now here let us assume the length of each card  = m units

The width of each card  = n units

Area of the given figure  = 180 sq units

Here, consider the given figure:

Here, the length of the rectangle  =  width of 4 cards

= 4 x ( Width of 1 card)  = 4 x ( n) =  4 n

Also, Here, the length of the rectangle  =  width of 1 card + Length of 1 card

                                                                  = m + n

AREA OF THE RECTANGLE  = LENGTH x WIDTH

⇒ 180   = 4 n ( m +  n)  .... (1)

Also, area of 1 card  = Length x width  = m x n   = mn

So, area of 9 such cards  = 9 x (m n) = 9  n m

AREA OF 9 RECTANGLES  = AREA OF THE FIGURE

⇒  9  n m = 180   .... (2)

Now, solving (1 ) and (2) fro values of m ,n we get:

Divide (1) by (2),  and solve , we get:  n = 5 units

Solving for m: 9 ( 5)  m = 180  , ⇒ m = 4 units

Now, the perimeter of figure  = Sum of all sides

= 2 (  m+ n) + 4n +  5m = 2(9) + 4(5) + 5(4)  = 18 + 20 +  20 = 58

Hence the perimeter of the given figure is 58 units.

the answer is d

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