Question

A rectangular picture frame with a perimeter of 3 meters has a height 2/3 times its width. Find the dimensions of the frame.

A. Width = 1 meter, Height = 2/3 meter
B. Width = 2/3 meter, Height = 1 meter
C. Width = 1/2 meter, Height = 1.5 meters
D. Width = 1.5 meters, Height = 1/2 meter

Answer 1

The dimensions of the frame are Width = 1 meter and Height = 2/3 meter.

Step-by-step explanation:

Let's assume the width of the frame is x meters.

Since the height is 2/3 times the width, the height of the frame would be (2/3)x meters.

The perimeter of a rectangle is given by the formula: P = 2(w + h), where P is the perimeter, w is the width, and h is the height.

Using the given information, we can write the equation: 3 = 2(x + (2/3)x)

Simplifying the equation, we have: 3 = 2(5/3)x

Dividing both sides of the equation by 2(5/3), we get: x = 3/(2(5/3))

Simplifying further, x = 1 meter.

Therefore, the dimensions of the frame are Width = 1 meter and Height = 2/3 meter.