Question

7. Nine playing cards from the same

Answer 1

Answer:

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.