Answer :
Final answer:
To find the dimensions of the painting with a perimeter of 112 feet and the length being 8 feet more than its width, we set up and solve the equation 2(w + 8) + 2w = 112, revealing the width to be 24 feet and the length to be 32 feet.
Explanation:
The question asks to find the dimensions of a painting on the world’s largest easel that has a perimeter of 112 feet, where its length is 8 feet more than its width. To solve this problem, let's denote the width of the painting as w feet. Therefore, its length will be w + 8 feet. Using the formula for the perimeter of a rectangle, which is P = 2l + 2w, we can set up the equation 2(w + 8) + 2w = 112.
Solving this equation step by step:
- First, expand the equation: 2w + 16 + 2w = 112.
- Combine like terms: 4w + 16 = 112.
- Subtract 16 from both sides: 4w = 96.
- Divide both sides by 4: w = 24.
Now that we know the width is 24 feet, to find the length, add 8 to the width:
Length = 24 + 8 = 32 feet. Hence, the dimensions of the painting are 24 feet by 32 feet.
