Answer:
The dimensions of the frame must be 13 inches and 6 inches
Step-by-step explanation:
* <em>Lets explain how to solve the problem</em>
- The perimeter of any quadrilateral is the sum of the lengths of its sides
- The rectangle is a quadrilateral with each two opposite sides are
equal so the perimeter of the rectangle = 2l + 2w, l and w are the
length and the width of it
- Candice has 38 inches of trim
- She wants to make a picture frame
- The frame is shaped a rectangle where its length is 5 inches less
than three times the width
- <u><em>Assume that the length is l and the width is w are the dimensions</em></u>
<em> </em><u><em>of the frame</em></u>
∵ l = 3w -5 ⇒ (1)
∵ The perimeter of the frame is the length of trim
∵ The length of the trim is 38 inches
∴ The perimeter of the frame is 38 inches
∵ Perimeter of the frame = 2l + 2w
∴ 2l + 2w = 38 ⇒ (2)
- <u><em>Substitute equation (1) in equation (2)</em></u>
∴ 2(3w - 5) + 2w = 38
- <em>Multiply the bracket by 2 and add like terms</em>
∴ 6w - 10 + 2w = 38
∴ 8w - 10 = 38
- <em>Add 10 for both sides</em>
∴ 8w = 48
- <em>divide both sides by 8</em>
∴ w = 6
- <u><em>Substitute the value of w in equation (1) to find l</em></u>
∵ l = 3w - 5
∴ l = 3(6) - 5 = 18 - 5 = 13
∴ l = 13
∵ l and w represent the length and the width of the frame
∴ The dimensions of the frame must be 13 inches and 6 inches
