Question

the length of a rectangle is five times its width. If the perimeter of the rectangle is 84 in, find its length and width

Answer 1

width=14 &Length = 70( can add unit behind the answer e.g.cm or mm etc..)

Explanation:

we know that in a rectangle not all side are same compare to a square..

therefore:

1) write the formula for perimeter down

perimeter = the sum of all side

perimeter = 2x(width) + 2x(length)

P=2(w)+2(L)

2) substitute into the equation

P =2(w)+2(L)

84=2(w)+2(5*w)

3) perform opposite operation to make w become the subject of the formula inorder to find width

48=2(w)+2(5*w)

48=2w+10w

48=12w

48/12=12w/12( the twelves cancels out)

7=w or the width is 7

4) rewrite the formula and solve

P=2(w)+2(L)

P =2(7) + 2(5*7)

P = 14 + 70

P = 48

Answer 2

Width = 7 in

Length = 35 in


You don't know what the width is, so you can give the value for width as x, where x is an unknown value to be found. The length is five times the width, so it can be written as 5x.

Width = x
Length = 5x

The perimeter is given as 84. The perimeter of a rectangle is:

Perimeter = 2(width) + 2(length)

Substitute the values for width, length and perimeter, then solve the equation to find x.

Perimeter = 2(width) + 2(length)

84 = 2(x) + 2(5x)

84 = 2x + 10x

84 = 12x

x = 7


Substitute the value of x = 7 to find the length and the width of the rectangle.

Width = x

Width = 7 in


Length = 5x

Length = 5(7)

Length = 35 in