Question

The area of a rectangular piece of land is 240 square meters. If the length of the land was 5 meters less and the width was 3 meters more, the shape of the land would be a square.

Part A: Write an equation to find the width (x) of the land. Show the steps of your work. (5 points)

Part B: What is the width of the land in meters? Show the steps of your work. (5 points)

Answer 1

@sammixboo @kropot72 @CGGURUMANJUNATH @sleepyjess

Answer 2

Let the length be y meters.
Let the width be x meters.
From the given information we can write the following:
y -5 = x + 3 ............(1)

@knightmare6 Do you want me to take you thru it step by step?

Answer 3

yes please if you can

Answer 4

helloo? @kropot72

Answer 5

@confluxepic

Answer 6

Rearranging equation (1) we get:
y = x + 8 .................(2)

The area is given by:
xy = 240 ............(3)
Rearranging (3) gives:
\[\large x=\frac{240}{y}\ ..............(4)\]
We can now substitute the expression for y in equation (2) into equation (4) giving:
\[\large x=\frac{240}{x+8}\ ..........(5)\]

Answer 7

Now if you cross-multiply equation (5) and rearrange you will be able to obtain a quadratic that can be solved for x.

Answer 8

cross multiply what?

Answer 9

Cross-multiplying (5) gives:
x(x + 8) = 240 ...........(6)
Now a quadratic can be formed from (6)

Answer 10

x^2+8x=240

Answer 11

Correct, so far. Then rearrange to give:
x^2 + 8x -240 = 0 ..........(7)
This is a quadratic which can be solved to find the value of x.

Answer 12

so thats my answer for A?

Answer 13

I believe that is sufficient for Part A, the reason being that Part B requires you to solve the quadratic.

Answer 14

so i got x=-4?

Answer 15

Is that correct i did -b/2a which is -8/2 and that means x=-4

Answer 16

Factorizing equation (7) gives:
(x + 20)(x - 12) = 0 ...........(8)
Can you find the value of x now?

Answer 17

what

Answer 18

that foiled is x^2+8x-240

Answer 19

Exactly! What values of x satisfy equation (8)?

Answer 20

uhmm idk

Answer 21

12 would and -20

Answer 22

What is the result if we plugged the value of -20 for x in equation (8)?

Answer 23

0

Answer 24

Yes x = -20 or 12. A negative value for the width x is ridiculous, so what must the value of x be?

Answer 25

12

Answer 26

Correct. x = 12 meters.