If the perimeter and the breadth of a rectangle are 54 cm and 7 cm, respectively, then its area =________ cm2.
Answers
Answer:
The ratio between the perimeter and the breadth of a rectangle is 5:1. If the area of the rectangle is 216 square cm, what is the length of the rectangle?
Let the rectangle be of length x and breadth y.
Perimeter = 2 ( length + breadth)
= 2 (x + y)
As per statement, the ratio between the perimeter and the breadth of a rectangle is 5:1.
Ratio between perimeter and breadth
2(x + y)/ y = 5 / 1
2x + 2y / y = 5 / 1
2x + 2y = 5y
2x = 5y - 2y
2x = 3y
x = 3y/2…Eq…1
The area of the rectangle is 216 square cm,
Area = length × breadth
xy = 216…Eq..2
Now putting the value of x from Eq..1 to Eq..2
xy = 216
3y/2 × y = 216
3y^2 = 216 × 2
3y^2 = 432
y^2= 432/3
y^2 = 144
y =√144
y = 12 cm.
The breadth if rectangle is 12 cm.
Now calculating length of rectangle by putting the value of y in Eq…2
xy = 216
x × 12 = 216
x = 216/12
x = 18 cm.
The length of rectangle is 18 cm.
The width of rectangle is 12 cm
Answer the length of rectangle is 18 cm.
Now checking the correctness of answer by putting the derived values of x and y in Eq..2
xy = 216 sq. cm.
18 × 12 = 216 sq. cm.
216 = 216 sq. cm.
Answer:
140 cm²
Step-by-step explanation:
explanation is in paper
