what are the dimensions of a rectangle if the perimeter is 24 and the width is 30 less than 5x the Length?

Answer 1

P = 2L + 2W = 24
W = 5L - 30
P = 2L + 2(5L -30) = 24
24 = 12L - 60
84 = 12L
7 = L
W = 5*7 - 30 = 5

Answer 2

let x = the longer side (the lenghth)
y = the shorter side (the width)

you know that if x is one of the sides and y is the other, and there are two of each side length (2x and 2y), so
2x+2y=24

you also know that the width (y) is (=) 30 less than 5
times x (5x-30)
so you know that y=5x-30

your two equations are
2x+2y=24
y=5x-30

since we know what y equals (5x-30), we can plug it into
the first equation to get
2x + 2y = 24
2x + 2(5x - 30) = 24
2x + 10x - 60 = 24
12x - 60 = 24
12x = 84
6x = 42
3x = 21
x = 7

so know that we know that the length is 7, we can plug that
into the original equation
2x + 2y = 24
2(7) + 2y = 24
14 + 2y = 24
2y = 10
y = 5

and the width is 5

so, the long side is 7, and the short side is 5

the dimensions are 5 x 7
the area is 35