Marcus is building a rectangular box for his kitten to sleep in. He wants the area of the bottom of the box to be 360 square inches and the length of one side to be 1 3/5 the length of the other side. What should the dimensions of the bottom of the bed be?
To find the dimensions of the bottom of the bed, we need to set up an equation based on the given information.
Let's assume the length of one side is "x" inches. The length of the other side would then be 1 3/5 times "x".
Since the area of the bottom of the box is 360 square inches, we can set up the following equation:
x * (1 3/5 * x) = 360
To simplify the equation, we can convert 1 3/5 to an improper fraction:
x * (8/5 * x) = 360
Now, let's simplify further by distributing:
8/5 * x^2 = 360
To isolate x^2, we can divide both sides of the equation by 8/5:
x^2 = 360 / (8/5)
To divide by a fraction, we can multiply by its reciprocal:
x^2 = 360 * (5/8)
Simplifying the right side:
x^2 = 225
Now, to find x, we can take the square root of both sides:
x = √225
x = 15
Therefore, the length of one side is 15 inches and the length of the other side is 1 3/5 times 15, which is 24 inches.
So, the dimensions of the bottom of the bed should be 15 inches by 24 inches.
You want one side to be s and the other side 1.6s
s*1.6s = 360
Solve for s and 1.6s
15 and 24?