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
2 answers
good job, you are correct
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
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