Question 996954
x is the base.
each side is x + 7/2 inches.
perimeter is 2 feet = 24 inches.
sum of the two sides is 2 * (x + 7/2) inches = 2x + 14/2 inches = 2x + 7 inches.


the sum of the two sides plus the base equals the perimeter.


x is the base and 2x + 7 is the sum of the two sides, so:


the perimeter = x + 2x + 7 = 24

combine like terms to get 3x + 7 = 24.
subtract 7 from both sides to get 3x = 17.
divide both sides by 3 to get x = 17/3 inches.


if x = 17/3 inches, then:


the base is equal to 17/3 inches.
the sum of the two sides is equal to 2 * 17/3 + 7 = 34/3 + 7 = 34/3 + 21/3 = 55/3 inches.


the perimeter is equal to the sum of the base plus the sum of the other two sides which is equal to 17/3 + 55/3 = 72/3 = 24 inches.


since we are already given that the perimeter is equal to 24 inches, then we have just confirmed that x = 17/3 is correct.


you were asked to find the length of the base.


the length of the base = x = 17/3 inches.


you can simplify this further if required to get the base = x = 5 and 2/3 inches.