Question

the length of a rectangle is 12m. lass than three times the width. the perimeter is 52cm. find the length of the rectangle

Answer 1

@mathstudent55

Answer 2

@misty1212

Answer 3

Let the width = w
Then the length is 3w - 12
Ok so far?

Answer 4

yes

Answer 5

There are two lengths with length 3w - 12, and two widths with length w.
Can you find the perimeter adding the lengths and the widths?

Answer 6

9w?

Answer 7

No.
Don't combine anything together.
Just write all the lengths and widths that you added together on a line.

Answer 8

3w-12+3 +3w-12 +w?

Answer 9

The two circled vertical sides are 3w - 12 + 3w - 12
The other two sides are w + w
When you put it all together, you get:

3w - 12 + 3w - 12 + w + w

Ok?

Answer 10

yea that makes more sense.

Answer 11

When you add the lengths of all sides, you get the perimeter.
That expression we just got is the perimeter of the rectangle.
We are told the perimeter is 52, so we set the expression for the perimeter equal to 52:

3w - 12 + 3w - 12 + w + w = 52

Answer 12

That is the equation we get.
It is a linear equation in one single variable, w.
We can solve for w.

Answer 13

\(3w - 12 + 3w - 12 + w + w = 52 \)

We will solve it like we did before.

Step 1. Combine like terms on both sides.
In this case, there are like terms only on the left side, so let's work on the left side.

Answer 14

Add all terms in w: 3w + 3w + w + w
Add all numbers: -12 - 12

Answer 15

What do you get for the sum of the terms in w?

Answer 16

-24

Answer 17

no sorry just 24

Answer 18

The terms in w are in red. The plain numbers are in green.

\(\color{red}{3w} \color{green}{- 12} + \color{red}{3w} \color{green}{- 12} + \color{red}{w} + \color{red}{w} = 52\)

\(\color{red}{3w + 3w + w + w} \color{green}{-12 - 12} = 52\)

\(\color{red}{8w } \color{green}{-24} = 52\)

Answer 19

3w + 3w + w + w = 8w
-12 -12 = -24

Answer 20

Ok, now we have

\(8w - 24 = 52\)

Step 2.
Now we are ready for the next step.
We need to move the number, -24, to the right side.
To do that, we add 24 to both sides.

Answer 21

8w - 24 = 52
+24 +24
--------------
8w = 76

Ok so far?

Answer 22

right.

Answer 23

For the final step, divide both sides by 8.
You get w, the width.
Then multiply w by 3 and subtract 12 to find the length.

Answer 24

THANKS. :)