Question

lines whose point of intersection is i. explain.​

Answer 1

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.