Question

The length of a rectangle is four times its width. Twice the perimeter of that rectangle is 160 cm. Find the length and width of that rectangle.​

Answer 1

Answer:

Let w = the breadth or the width of the rectangle.

Since the length l is 4 times the breadth or width of the rectangle, then ...

l = 4w.

The formula for the perimeter P of a rectangle is:

P = 2l + 2w

Substituting for l in the formula for P, we have:

P = 2(4w) + 2w

P = 8w + 2w

P = 10w

Since its given that P = 200, then substituting for P, we get:

200 = 10w

10w = 200 (Since equality is symmetric, i.e., if a = b, then b = a)

(10w)/10 = 200/10

(10/10)w = 20

(1)w = 20

w = 20 and

l = 4w

= 4(20)

l = 80

CHECK:

P = 2l + 2w

200 = 2(80) + 2(20)

200 = 160 + 40

200 = 200

Therefore, the length and breadth (width) of the given rectangle are 80 and 20, respectively.