Answer :
The length and width of a rectangle are 36cm and 4.5cm
Finding the Width:
The formula to find the perimeter of the rectangle is:
P=2(l+w),
where P is the perimeter, l be the length, and w be the width.
Now substitute the given values to solve for w, since we need to find the width.
The given information is:
the length of a rectangle is six inches more than eight times the width so the equation becomes:
L=8w+6
P=120
w=8w
now plug the values in the above formula:
P=2(l+w),
120=2(8w+6)+8w
120=16w+12+8w
120=24w+12
24w=108
w=4.5
To find the length just substitute in the L.
L=8(4.5)+6
L=30+6
L=36
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To find the length and width of the rectangle, we set up an algebraic equation using the perimeter formula and the relation between length and width. We found the width to be 6 inches and the length to be 54 inches.
Let's denote the width of the rectangle as w inches. Therefore, the length of the rectangle will be 8w + 6 inches. The formula for perimeter P of a rectangle is P = 2l + 2w, where l is length and w is width. We can set up the equation 120 = 2(8w + 6) + 2w to represent the given perimeter.
Solving this equation:
First, distribute the 2 into the parentheses: 120 = 16w + 12 + 2w.
Combine like terms: 120 = 18w + 12.
Subtract 12 from both sides: 108 = 18w.
Divide both sides by 18: 6 = w.
Now that we have the width, we can find the length by substituting w with 6 in the length expression 8w + 6, which gives us: length = 8(6) + 6 = 48 + 6 = 54 inches.
Therefore, the width of the rectangle is 6 inches and the length is 54 inches.
