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
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
To find the length of the rectangle, we can use the formula for the perimeter of a rectangle: P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.
Given that the perimeter is 80 cm, we can substitute P = 80 into the formula: 80 = 2L + 2W.
We are also given that the width is 2/3 of the length. So we can express the width as W = (2/3)L.
Substituting this expression for W into the equation for the perimeter, we have: 80 = 2L + 2((2/3)L).
Simplifying the equation: 80 = 2L + (4/3)L.
To combine the terms with L, we need a common denominator for 2 and 4/3, which is 3. So the equation becomes: 80 = (6/3)L + (4/3)L.
Combining the L terms, we have: 80 = (10/3)L.
To isolate L, we can multiply both sides of the equation by 3/10: (80 * 3/10) = L.
Simplifying: 24 cm = L.
Therefore, the length of the rectangle is 24 cm.
To find the width, we can substitute this value back into the expression for W: W = (2/3) * L = (2/3) * 24 = 16 cm.
So the dimensions of the rectangle are length = 24 cm and width = 16 cm.