Application problem

Question

One side of a rectangle is 20 km longer than ten times another side. Find the length of the sides, given that the area of the rectangle is 1200 km².

1. Length of sides=?

Answer 1

Hello Angel,

First, let's assign some terms or expressions to the sides of the rectangle, fair enough? Also, when working these problems, I encourage you to draw a rectangle to give yourself a better picture of what you are trying to get at (for yourself).

So:

Let one side be x

Let another side be 10x + 20

Now, we know the formula for the area of a rectangle is as follows:

A = L x W Where A equals area, L equals length, and W equals width.

According to the problem: We know the area to be 1200 km ^2

1200 = x * 10x + 20

1200 = 10x^2 + 20

120 = x^2 + 20

100 = x^2

x = 10 <-----Length of one side

10(10) + 20 = 120 <------Length of the other side

Now, let's check our work, okay?

A = L x W

1200 = 10 * 120

1200 = 1200

For added information, the formula for a perimeter is P = 2 (L + W) or P = 2(L) + 2(W) Where P equals perimeter, L equals length and W equals width. Also, please note that the second formula is the same as the first with the only difference being the distributive property of math being applied.

P = 2(10) + 2(120)

P = 20 + 240

P = 260

I hope the information assists and that I have given you the assistance you need. I wish you a great week and please feel free to contact me or any tutor should you need further assistance.

Answer 2

Area of a rectangle is length * width or L*W. From the first sentence, L = (10*W) + 20. Therefore:

1200 = L*W = (10*W)+20)*W = 10W^2+20W

0 = 10W^2+20W-1200 = W^2+2W-120 = (W+12)*(W-10) which has solutions of W=-12 and W=10

Since a rectangle cannot have a negative width, the width is 10km and the length (10*10)+20=120km