A rectangle has a width that is 1/8 its length. If the perimeter of the rectangle is 126 inches, what is the width of the rectangle?
You were given:
A rectangle has a width that is 1/8 its length. If the perimeter of the rectangle is 126 inches, what is the width of the rectangle?
Length = we don't know and so I'll call it x.
Width = 1/8(x), which can be written x/8.
The perimeter given is 126 inches.
We use the formula for finding the perimeter of a rectangle.
P = 2L + 2W, where P = perimeter, L = length and W = width.
Is this clear so far?
126 inches = 2(x) + 2(x/8)
I will not use the word inches again for P because you know we are talking about a perimeter of 126 inches, right?
126 = 2x + x/4
We now have a fractional equation.
How do we remove the fraction part?
We multiply each term by the LCD, which so happens to be 4.
126(4) = 2x(4) + (x/4)(4)
504 = 8x + x
504 = 9x
To find x, we divide BOTH sides of the equation by 9.
504 divided by 9 = x
56 = x
We are looking for the width, right?
The width is (1/8)(x), which can also be written x/8.
We just found x, right?
To find the width, replace x with 56 in the fraction x/8 and then divide the numerator by the denominator.
So, x/8 becomes 56/8 = 7
What is the width of this rectangle?
Final answer: 7 inches.
That's it!
Let's denote the length of the rectangle as L and the width as W.
According to the given information, we can write:
W = (1/8)L
The formula for the perimeter of a rectangle is given by:
Perimeter = 2(L + W)
Substituting the value of W from the first equation into the perimeter formula, we get:
126 = 2(L + (1/8)L)
Simplifying further:
126 = 2(9/8)L
Using the distributive property, we can rewrite it as:
126 = (18/8)L
Now, let's solve for L:
L = (126 * 8) / 18
L = 56
Substituting this value of L back into the first equation, we can solve for W:
W = (1/8)*(56)
W = 7
Therefore, the width of the rectangle is 7 inches.
To solve this problem, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (Length + Width)
Let's denote the length of the rectangle as L, and the width as W. Given that the width is 1/8 of the length, we have:
W = (1/8) * L
Substituting this into the formula for the perimeter, we get:
126 = 2 * (L + (1/8) * L)
To simplify the equation, let's first multiply both sides by 8 to get rid of the fraction:
1008 = 16L + 2L
Combine the terms on the right side:
1008 = 18L
Now, divide both sides by 18 to solve for L:
L = 1008 / 18 = 56
So, the length of the rectangle is 56 inches. To find the width, substitute this value back into the equation W = (1/8) * L:
W = (1/8) * 56 = 7
Therefore, the width of the rectangle is 7 inches.
l=8w
126=2l+2w
126=2l+2*1/8 l
126=2l+ l/4 l=2.25 l
solve for l, then w.