The length of a rectangle is 3 meters more than 3 times the width. If the area is 126 square meters, find the width and length

Answer 1

Hi, Houda.

Okay, so you know that the length of the rectangle is 3 meters more than 3 times the width.

So, let the width be w.

Then the length (l) = 3w + 3

So, then the area is l x w = (3w + 3)w = 126

So, to solve you get

3w² + 3w = 126

3w² + 3w - 126 = 0

3(w² + w - 42) = 0

w² + w - 42 = 0

(w + 7)(w - 6) = 0

The solutions to this equation are w = -7, 6

Since you can't have a negative length, the answer is w = 6 meters

Now, check your answer

length = 3w + 3 = 3x6 + 3 = 21

6 x (21) = 126 sq. meters

So the answer is width = 6 meters

and the length is 21 meters

Answer 2

Given the information above, we can make an equation to find the values of the rectangle's length and width.

If the length is 3 meters more than 3 times the width, we can write that as L = 3W + 3 where L is length and W is width

We can also note that L * W = 126

To find the length and width, we first will need to find the width by making the equation above have only one variable (width)

The equation alternatively written looks like (3W + 3) * W = 126

distribute the W to get 3W² + 3W = 126

Subtract 126 to get all factors on the same side

3W² + 3W - 126 = 0

We can take out the greatest common factor of 3 to make things easier

W² + W - 42 = 0

Now we need to factor by finding a set of numbers which add to 1 (the W has a 1 multiplied to it) and multiply to 42

In this case, the numbers are 6 and 7

Because 6 - 7 = -1, we will want to have 6 be negative and 7 positive (-6 + 7 = 1)

Now we have (W - 6)*(W + 7) = 0

Each one will become its own equation

W - 6 = 0 W + 7 = 0

W = 6 W = -7

Because our width can't be negative, we know only the W = 6 can be true.

Now we can use our width of 6 to find the Length by using the equation L = 3W + 3

L = 3*6 + 3

L = 18 + 3 = 21