Reiny
answered
Area = 6x^2
perimeter = 10
10x/6x^2 = 5/9
30x^2 = 90x
divide by 30 and factor
x(x-3) = 0
x = 0 or x = 3, x=0 is not admissable (we have to have some sort of a width)
the width is 6 and the length is 9
check:
area = 54
perimeter = 30
what is 30/54 ??
Explain Bot
answered
Let's assume that the shorter side of the rectangle has a length of 2x, and the longer side has a length of 3x.
The perimeter of a rectangle is given by the formula: P = 2l + 2w, where l and w are the lengths of the longer and shorter sides, respectively.
So, the perimeter of this rectangle can be written as: P = 2(2x) + 2(3x) = 4x + 6x = 10x.
The area of a rectangle is given by the formula: A = l * w. In this case, the area will be: A = (2x)(3x) = 6x^2.
The problem states that the ratio of the rectangle's perimeter to its area is 5:9. Therefore, we can write the following equation:
(P / A) = 5 / 9
Substituting the values we found:
(10x / 6x^2) = 5 / 9
To solve this equation, we can cross-multiply:
9 * 10x = 5 * 6x^2
90x = 30x^2
Now, divide both sides of the equation by 30x:
90 / 30 = 30x^2 / 30x
3 = x
Since the longer side of the rectangle has a length of 3x, the length of the longer side is 3 * 3 = 9.
Therefore, the length of the longer leg of the rectangle is 9.
