Question

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

Answer 1

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

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.