Question
The length of a rectangle is nine more than triple the width. If the perimeter is 106 inches, find the dimensions.
298
likes1490 views
Answer to a math question The length of a rectangle is nine more than triple the width. If the perimeter is 106 inches, find the dimensions.
Tiffany
4.5103 Answers
1. Let the width of the rectangle be w
2. Then the length of the rectangle is 3w + 9
3. The formula for the perimeter of a rectangle is P = 2l + 2w
4. Substituting the given perimeter and expressions for length and width:
106 = 2(3w + 9) + 2w
5. Simplifying the equation:
106 = 6w + 18 + 2w
106 = 8w + 18
6. Subtract 18 from both sides:
106 - 18 = 8w
88 = 8w
7. Divide both sides by 8:
w = 11
8. Now calculate the length using l = 3w + 9
l = 3(11) + 9
l = 33 + 9
l = 42
9. Therefore, the dimensions are:
Width: w = 11
Length: l = 42
2. Then the length of the rectangle is
3. The formula for the perimeter of a rectangle is
4. Substituting the given perimeter and expressions for length and width:
5. Simplifying the equation:
6. Subtract 18 from both sides:
7. Divide both sides by 8:
8. Now calculate the length using
9. Therefore, the dimensions are:
Width:
Length:
Frequently asked questions (FAQs)
Math Question: Find the absolute extrema of the function f(x) = x^3 - 6x^2 + 9x + 2 on the interval [-2, 4].
+
Question: What is the integral of f(x) = 3x^2 + 2x - 5 from x = 1 to x = 4?
+
Question: For a circle with equation x^2 + y^2 = r^2, if the radius is 5, find the value of y when x = 3.
+
New questions in Mathematics