The length of a rectangle is 3x+10 feet and its width is x+12 feet. If the perimeter of the rectangle is 76 feet, how many square feet are in the area of the rectangle?
352 actually
To find the area of the rectangle, we need to multiply its length by its width.
We are given that the length of the rectangle is 3x + 10 feet and the width is x + 12 feet.
So, the area (A) of the rectangle can be calculated as:
A = (3x + 10) * (x + 12)
Now, let's find the values of x that satisfy the given condition of the perimeter being 76 feet.
The perimeter of a rectangle is obtained by adding the lengths of all its sides. For a rectangle, the perimeter (P) can be calculated as:
P = 2 * (length + width)
We are given that the perimeter is 76 feet. So, we have the equation:
76 = 2 * ((3x + 10) + (x + 12))
Simplifying the equation further:
76 = 2 * (4x + 22)
38 = 4x + 22
16 = 4x
x = 4
Now, we substitute the value of x back into the area equation A = (3x + 10) * (x + 12):
A = (3 * 4 + 10) * (4 + 12)
A = 22 * 16
A = 352
Therefore, the area of the rectangle is 352 square feet.
just solve
2(3x+10 + x+12) = 76
then you can figure the length and width, and thus the area.