A storage shed is in the shape of a square. A builder increases the length of one side of the shed by three feet and decreases the length of an adjacent side by two feet. The shed is now a rectangle with a perimeter of 70 feet. What is the measure of a side of the original shed? [ Only an algebraic solution will be accepted ]
at first:
let x be the length of the side of the square.
after the change:
new length = x+3
new width = x-2
perimeter = 2(x+3) + 2(x-2)
= 70
simplify the equation and solve for x
12.63
To solve this problem algebraically, let's denote the original side length of the shed as x.
According to the problem, the builder increases one side of the shed by 3 feet, so the length of the new rectangle is (x + 3). The builder also decreases the adjacent side by 2 feet, so the width of the new rectangle is (x - 2).
The perimeter of a rectangle is calculated by adding up all the side lengths. Therefore, the perimeter of the new rectangle is given as:
2 * (x + 3) + 2 * (x - 2) = 70.
Simplifying the equation, we can distribute the multiplication:
2x + 6 + 2x - 4 = 70.
Combining like terms, we have:
4x + 2 = 70.
Subtracting 2 from both sides to isolate the term with x:
4x = 68.
Then, dividing both sides by 4 to solve for x:
x = 17.
Therefore, the measure of a side of the original shed is 17 feet.