Question

Perimeter of a rectangle is 70 meters and area is 300sq.m.

(a)What s the sum of the length and breadth of the rectangle?

(b)If length is ‘x' then what is breadth?

(c)Write the equation to find the area of the rectangle using the above length

and breadth.

(d) Find the length and breadth of the rectangle.​

Answer 1

Step-by-step explanation:

Given: Rectangular Area = 300 sq. m. = L x W

Perimeter = 70 m = 2 L + 2 W

Find: length and width

Either formula can be used with the other formula to help.

From P => (70 - 2W)/2 = L

Now substitute into the area formula.

300 = [(70 - 2W)/2] x W simply and solve

300 = (35 - W) x W Therefore

300 = 35W - W^2. Or

W^2 - 35W + 300 = 0

(W - 20)(W - 15) = 0 =>

W - 20 = 0 or W - 15 = 0 Therefore: W = 20 or W = 15

If W = 20 L = (70 - 2(20))/2 = (70 - 40)/2 = 30/2 = 15

If W = 15 L = (70 - 2(15))/2 = (70 - 30)/2 = 40/2 = 20

Solutions: Width = 20 m, Length = 15 m or

vice versa Width = 15 m, Length = 20 m

You can easily check:

A = L x W = 15 m x 20 m = 300 m^2 = 20 m x 15 m

P = 2L + 2W = 2(15m) + 2(20m) = 70 m = 2(20m) + 2(15m) hope it helps you