A rectangle has width the same asa a side of a square whose perimeter is 20m.the length of the rectangle is 9m. Find the perimeter of this rectangle.
34. The with of a rectangular picture is on-half the length . The perimeter of the rectangle is 72inches. Fid the length of the picture.
35. The width of a rectangular playground is 18 meters less than the length . Find the width when the perimeter of the rectangle is 84.
40. The length of a rectangular picture is seven inches longer than the width . find the length and width if the perimeter of the picuter is 62 iches.
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To solve these problems, we need to first understand the given information and then apply the appropriate formulas.
Let's tackle each problem step by step:
34. The width of a rectangular picture is one-half the length. The perimeter of the rectangle is 72 inches. Find the length of the picture.
- Let's denote the width of the rectangle as 'w' and the length as 'l'.
- According to the given information, we know that w = (1/2)l.
- The perimeter of the rectangle is calculated using the formula P = 2w + 2l.
- Substituting w = (1/2)l, we can rewrite the perimeter equation as P = 2(1/2)l + 2l.
- Simplifying, we have P = l + 2l = 3l = 72.
- Divide both sides of the equation by 3 to solve for l: l = 72/3 = 24.
- Therefore, the length of the picture is 24 inches.
35. The width of a rectangular playground is 18 meters less than the length. Find the width when the perimeter of the rectangle is 84.
- Let's denote the width of the rectangle as 'w' and the length as 'l'.
- According to the given information, we know that w = l - 18.
- The perimeter of the rectangle is calculated using the formula P = 2w + 2l.
- Substituting w = l - 18, we can rewrite the perimeter equation as P = 2(l - 18) + 2l.
- Simplifying, we have P = 2l - 36 + 2l = 4l - 36 = 84.
- Add 36 to both sides of the equation: 4l = 84 + 36 = 120.
- Divide both sides of the equation by 4 to solve for l: l = 120/4 = 30.
- Substitute the value of l back into the equation w = l - 18 to find w: w = 30 - 18 = 12.
- Therefore, the width of the rectangular playground is 12 meters.
40. The length of a rectangular picture is seven inches longer than the width. Find the length and width if the perimeter of the picture is 62 inches.
- Let's denote the width of the rectangle as 'w' and the length as 'l'.
- According to the given information, we know that l = w + 7.
- The perimeter of the rectangle is calculated using the formula P = 2w + 2l.
- Substituting l = w + 7, we can rewrite the perimeter equation as P = 2w + 2(w + 7).
- Simplifying, we have P = 2w + 2w + 14 = 4w + 14 = 62.
- Subtract 14 from both sides of the equation: 4w = 62 - 14 = 48.
- Divide both sides of the equation by 4 to solve for w: w = 48/4 = 12.
- Substitute the value of w back into the equation l = w + 7 to find l: l = 12 + 7 = 19.
- Therefore, the width of the rectangular picture is 12 inches, and the length is 19 inches.
I hope this explanation helps you solve the problems. Let me know if you have any further questions!