A rectangle has a perimeter of 40 feet. The length is 4 feet longer than the width. Find the dimensions of the rectangle.
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In the problem, the length is being compared to the width. So, let x be the width of the rectangle.
width = x
Then, express in math form the condition "the length is 4 ft longer than the width".
length = x + 4
To set-up the equation, apply the formula of perimeter of rectangle.
`P = 2 * (L + W)`
where L is the length and W is the width.
Plugging in the length and width of the given rectangle, the formula becomes:
`P = 2((x+4)+x)`
Also, plug-in the given perimeter P=40.
Hence, the equation is:
`40=2((x+4)+x)`
Simplifying the right side, it becomes:
`40=2(2x+4)`
`40=4x+8`
Isolating the x result in:
`32=4x`
`8=x`
So, the width is 8. And, its length is:
length` =x + 4 = 8 + 4 =12`
Therefore, the rectangle has a length of 12 feet and a width of 8 feet.
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A rectangle has a perimeter of 40 feet. The length is 4 feet longer than the width. Find the dimensions of the rectangle. The formula for the perimeter of a rectangle is 2l + 2w= Perimeter. Or you can add up all the sides together.
Let's call the width=w.
Since the length is 4 feet longer than the width, the equation for the length would be:
(4+w). Using the perimeter equation we can solve:
2(4+w) + 2(w)=40
8+2w+2w=40
8+4w=40
w=8. Therefore, the width is 8. Since length is 4+w, it's 4+8 which equals 12. So, the width is 8 feet and length is 12.
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