Q:

URGENT!! PLEASE ANSWER!After completing the wood trim on her kitchen​ cabinets, Candice has 38 inches of trim left. She decides to make a picture frame out of the wood. She wants to make the frame so that the length is 5 inches less than three times the width. What must the dimensions​ be?

Accepted Solution

A:
Answer:The dimensions of the frame must be 13 inches and 6 inches Step-by-step explanation:* Lets explain how to solve the problem- 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- Assume that the length is l and the width is w are the dimensions  of the frame∵ 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)- Substitute equation (1) in equation (2)∴ 2(3w - 5) + 2w = 38- Multiply the bracket by 2 and add like terms∴ 6w - 10 + 2w = 38∴ 8w - 10 = 38- Add 10 for both sides∴ 8w = 48- divide both sides by 8∴ w = 6- Substitute the value of w in equation (1) to find l∵ 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