Question

A rectangle has a width which is 2/3 of its length. Find its length if its perimeter is 80 cm. Find its dimensions.
P = 2L + 2W
80cm = 2L + 2 (2/3)L
80cm =6/3 L + 4/3L
80cm = 10/3 L
80. 3/10 = L
24cm =L or L= 24 cm W = 2/3 .24
W = 16 cm

Answer 1

good job, you are correct

Answer 2

Let the Length of the rectangle be x and width as y.

As per statement width of the rectangle is 2/3 of its length.Accordibgly

y = 2/3 × x …Eq..1

Perimeter of a rectangle = 2 (Length + width)

Perimeter is given as 80 cm.

2 (x + 2/3y) = 80

2 × x (1 + 2/3) = 80

x = 80 / [2 (1 + 2/3)]

x = 80 / (2 (5/3)

x = 80 / [10/3]

x = 3 × 80/ 10

x = 240/10

x = 24

Length of rectangle is 24 centimeter

Now calculating width as per Eq..1

y = 2/3 × x

y = 2/3 × 24

y = 48 / 3

The width of rectangle is 16

Area of rectangle is = Length × width

Substituting the value of length x and width y

Area of rectangle = 24 × 16

Area of rectangle = 384 square centimeter