Question

the length of a rectangle is 6 more than half of its width. The perimeter is 36 inches. Find the dinensions of the rectangle.​

Answer 1

To find the dimensions of the rectangle, set up an equation using the given information. Solve for the width and substitute it back into the equation for length to find the dimensions.

Step-by-step explanation:

To find the dimensions of the rectangle, we can set up an equation using the given information. Let's say the width of the rectangle is x inches. The length of the rectangle is 6 more than half of its width, so it would be (x/2) + 6 inches. The perimeter of a rectangle is given by the formula P = 2(length + width). We can plug in the given values and solve for x:

1. Given: P = 36 inches
2. Equation: 36 = 2((x/2) + 6 + x)
3. Simplify: 36 = 2x + 12 + 2x
4. Combine like terms: 36 = 4x + 12
5. Subtract 12 from both sides: 24 = 4x
6. Divide both sides by 4: x = 6

So the width of the rectangle is 6 inches. Substituting this value back into the equation for length, the length would be (6/2) + 6 = 3 + 6 = 9 inches. Therefore, the dimensions of the rectangle are 6 inches by 9 inches.