Question
the lengths of the sides of rectangular window have the ratio 2.5 to 1 the area of window is 2,250 square inches what are the dimensions of the window
A 30inches by 75 inches
B 60 inches by 37.5 inches
C 30 inches by 45inches
D 50 inches by 45inches
A 30inches by 75 inches
B 60 inches by 37.5 inches
C 30 inches by 45inches
D 50 inches by 45inches
Answers
GPT 3.5
Let's assume that the shorter side of the rectangle is x inches.
According to the given ratio of 2.5 to 1, the longer side would be 2.5x inches.
The area of the rectangle is length × width = x × 2.5x = 2.5x^2.
We are given that the area is 2,250 square inches, so:
2.5x^2 = 2,250
Dividing both sides of the equation by 2.5:
x^2 = 900
Taking the square root of both sides:
x = 30
Therefore, the dimensions of the window are:
Shorter side: 30 inches
Longer side: 2.5x = 2.5(30) = 75 inches
So, the correct answer is A) 30 inches by 75 inches.
According to the given ratio of 2.5 to 1, the longer side would be 2.5x inches.
The area of the rectangle is length × width = x × 2.5x = 2.5x^2.
We are given that the area is 2,250 square inches, so:
2.5x^2 = 2,250
Dividing both sides of the equation by 2.5:
x^2 = 900
Taking the square root of both sides:
x = 30
Therefore, the dimensions of the window are:
Shorter side: 30 inches
Longer side: 2.5x = 2.5(30) = 75 inches
So, the correct answer is A) 30 inches by 75 inches.