The lengths of the sides of a rectangular window have the ratio 1.5 to 1. The area of the window is 1,350 square inches. What are the dimensions of the window?
answer is 30 inches by 45 inches
please show work
Let's assume that the shorter side of the rectangular window is 1x, and the longer side is 1.5x.
The area of a rectangle is given by the formula: length x width.
Therefore, we can write an equation for the area of the window:
1x * 1.5x = 1,350
Simplifying the equation:
1.5x^2 = 1,350
Dividing both sides of the equation by 1.5:
x^2 = 900
Taking the square root of both sides:
x = √900
x = 30
Therefore, the shorter side of the window is 30 inches.
The longer side of the window is 1.5 times longer:
1.5 * 30 = 45
Therefore, the dimensions of the window are 30 inches by 45 inches.