The length of a rectangle is for more than three times the width of the rectangle. If the perimeter of the rectangle is 62 inches what are the length of the sides?

Question

what is the width of the rectangle?

what are the length of the rectangle?

Answer 1

Let us denote the Length of the rectangle with the variable L: L = Length

Let us denote the Width of the rectangle with the variable W: W = Width

It's much more simple to break this question down into steps.

1) The length of the rectangle is 4 more than

1. MORE THAN is a key phrase that means ADDITION
2. So 4 more than means + 4

2) Three times the width of the rectangle.

1. THREE TIMES THE WIDTH is our key phrase here meaning multiplication 3 x W or 3W

3) Make our first equation by using steps 1 and 2.

1. L = 3W + 4

4) They say the perimeter is 62 inches.

1. Perimeter ( P ) is the addition of all sides of a polygon. A rectangle has 2 lengths and 2 widths that need to be added.
2. So, P = 2L + 2W
3. So, 62 = 2L + 2W

5) Now we have 2 equations and 2 unknown variables. This makes it possible to solve for any variable we want and substitute the found value into another equation. Because we want to solve for Length we will first solve for Width in the step 4 equation.

1. 62 = 2L + 2W
2. Subtract both sides by 2L
3. 2W = 62 - 2L
4. Divide both sides by 2
5. W = 31 - L
6. Now we have an equation for W.

6) With our equation for W we can now solve for the value of L by substitution.

1. W = 31 - L
2. Sub into step 3.
3. L = 3 ( 31 - L ) + 4
4. We can now distribute 3 into 31 - L.
5. L = 93 - 3L +4
6. Gather like terms and simplify by adding 3L to both sides.
7. 4L = 97
8. Divide by 4.
9. L = 24.25 inches

7) Since we now know the Length of our rectangle we can solve for Width by plugging our Length value into our Width equation found in step 5.

1. W = 31 - L
2. plug in L
3. W = 31 - 24.25
4. W = 6.75 inches

8) As a check we can plug our values into the Perimeter equation we found in step 4. If we are correct we should get 62 inches.

1. 62 = 2L + 2 W
2. plug in L = 24.25 and W = 6.75
3. 62 = 2 ( 24.25 ) + 2 ( 6.75 )
4. 62 = 62 ! Looks like our values are correct!

HOPE THIS HELPED!