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