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

Expert Answers
justaguide eNotes educator| Certified Educator

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.

taangerine | Student

 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)
 
Let's find the length first. 
  • 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
To find width:
  • 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
Our dimensions are:
Length=15 m
And, Width=60 m
 
 
jess1999 | Student

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 .