Question

A frame around a family portrait has a perimeter of 90 inches. The

length is fifteen inches less than twice the width. Find the dimensions
(the length and the width) of the frame.

Answer 1

Using the given perimeter and the relationship between the length and width of the frame, the dimensions are calculated to be 25 inches in length and 20 inches in width.

Step-by-step explanation:

The task is to find the dimensions of a frame that has a perimeter of 90 inches where the length of the frame is fifteen inches less than twice the width of the frame. To solve this, let's denote the width of the frame as w inches. Therefore, the length will be 2w - 15 inches. The perimeter of a rectangle is the sum of all its sides - which is twice the length plus twice the width for a rectangle.

Now we set up an equation based on the perimeter:

• 2l + 2w = 90
• 2(2w - 15) + 2w = 90
• 4w - 30 + 2w = 90
• 6w - 30 = 90
• 6w = 120
• w = 20 inches

Since we now have the width, we can find the length:

• l = 2w - 15
• l = 2(20) - 15
• l = 40 - 15
• l = 25 inches

The dimensions of the frame are therefore 25 inches in length and 20 inches in width.

Answer 2

Let x be the width of the rectangular family portrait , then its length will be 2x-15.

I hope this is helpful!