the perimeter of a rectangular yard is 270 feet. If its length is 25 feet greater than its width what are the dimensions of the yard
P=2l+2w
270=2(w+25)+2w
270=2w+50+2w
220=4w
55=w
so
l=w+25
=55+25
=80
Check
P=2l+2w
270=2(80)+2(55)
270=160+110
270=270
To find the dimensions of the rectangular yard, we can set up a system of equations based on the given information.
Let's denote the width of the yard as "w" and the length as "l".
According to the problem, the length is 25 feet greater than the width:
l = w + 25 --- (Equation 1)
The perimeter of a rectangle is given by the formula: P = 2l + 2w, where P represents the perimeter.
We are given that the perimeter is 270 feet:
270 = 2l + 2w --- (Equation 2)
Now, we can solve the system of equations (Equation 1 and 2) simultaneously to find the values of "l" and "w".
Substitute the value of "l" from Equation 1 into Equation 2:
270 = 2(w + 25) + 2w
270 = 2w + 50 + 2w
270 = 4w + 50
Rearrange the equation:
4w = 270 - 50
4w = 220
Divide both sides of the equation by 4:
w = 220 / 4
w = 55
Now substitute the value of "w" back into Equation 1 to find the value of "l":
l = w + 25
l = 55 + 25
l = 80
Therefore, the dimensions of the yard are width = 55 feet and length = 80 feet.