the perimeter of a rectangle is 24 m. the width is 30 m less than five times the length. find the dimentions of the rectangle.
P = 2L + 2W
24 = 2L + 2(5L - 30)
24 = 2L + 10L - 60
84 = 12L
7 = L
To solve this problem, we need to set up equations based on the given information and then solve for the dimensions of the rectangle.
Let's assume the length of the rectangle is "L" meters and the width is "W" meters.
According to the problem, the perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
We know that the perimeter is given as 24 meters, so we can write the equation as:
24 = 2 * (L + W) ----(Equation 1)
We are also given that the width is 30 meters less than five times the length, which can be expressed as:
W = (5L - 30) ----(Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two unknowns (L and W). We can solve this system of equations using the substitution method or elimination method.
Let's use the substitution method to solve the system:
Substitute the value of W from Equation 2 into Equation 1:
24 = 2 * (L + (5L - 30))
24 = 2 * (6L - 30)
24 = 12L - 60
12L = 24 + 60
12L = 84
L = 84 / 12
L = 7
Now substitute the value of L back into Equation 2 to find W:
W = (5 * 7 - 30)
W = 35 - 30
W = 5
Therefore, the dimensions of the rectangle are: Length = 7 meters and Width = 5 meters.