Question

The length of a rectangular lot is 10 more than twice its width. If the area of the lot is 1,000 square meters, find the dimension of the lot.

Answer 1

Given :-

• The length of a rectangular lot is 10 more than twice its width.
• The area of the lot is 1,000 square meters.

To Find :-

• Find the dimension of the lot. ?

Solution :-

Let us assume that, the width of the rectangular lot is x m.

Than,

→ Length of rectangular lot = 2 * width + 10

→ Length of rectangular lot = (2x + 10) m.

So,

→ Area of rectangular lot = Length * Width

→ Area = (2x + 10) * x

Putting given value of area of lot, we get,

→ (2x + 10)x = 1000

→ 2(x + 5)x = 1000

Dividing both sides by 2,

→ x(x + 5) = 500

→ x² + 5x = 500

→ x² + 5x - 500 = 0

→ x² + 25x - 20x - 500 = 0

→ x(x + 25) - 20(x - 25) = 0

→ (x + 25)(x - 20) = 0

→ x = (-25) or 20.

Since, Negative value of width is not Possible.

Therefore,

→ width of rectangular lot = 20m. (Ans.)

→ Length of rectangular lot = (2x + 10) = (2*20 + 10) = 40 + 10 = 50m. (Ans.)

Hence, the dimension of the lot are 50m and 20m.