# A rectangle is four times as longer as it is wide. If the perimeter of the rectangle is 150m, what are its dimensions.

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### 3 Answers

The length of the rectangle is four times its width. Let the width of the rectangle be x, the length is 4x.

The perimeter of the rectangle is 4x + 4x + x + x = 10*x = 150

=> x = 15

**The dimensions of the rectangle are 15 m and 60 m.**

** WHAT DO WE KNOW**

*A rectangle is four times as longer as it is wide.***4l=w**

*The perimeter of the rectangle is 150m.***P=150 m**

**FORMULA FOR PERIMETER: P=2(l+w)**

- Plug-in 4l for w in Perimeter formula & P=150 : 150=2(l+4l)
- Simplify/Combine like terms: 150=2(5l)
- Multiply: 150=10l
- Opposite operation for multiplication? (division)-- Divide 10 from both sides to isolate l: `150/10 = (10l)/10`
- Simplify: 15=l, or l=15 m

- Plug-in l=15 & P=150 in the perimeter formula: 150=2(15+w)
- Distribute 2: 150=30+2w
- Subtract 30 from both sides to isolate '2w': 120=2w
- What is the opposite operation for multiplication? (division) -- Divide 2 on both sides to isolate 'w': `120/2 = (2w)/2`
- Simplify: 60=w, or w=60 m

To solve this word problem, use the equation

4x + 4x + x + x = 150 with " x " representing the width

Now combine all the like terms. By combining the like terms, you should get

10x = 150 now divide both sides by 10

By dividing on both sides, you should get

x = 15 which is one if the dimension

Now use 4x to find the length

4 ( 15 ) = 60

So your answer is width is 15 m and length is 60 m .