If the side of a square are extended to form a rectangle. One side of the square is extended by 5cm and the other side by 2cm. The area of the rectangle is 130cm^3. Find the length of the side of the square
"If the side of a square are extended to form a rectangle." ??
A sentence that begins with "If ..." must end with "then ...."
let the new sides be x+5 and x+2
(x+5)(x+2) = 130
x^2 + 7x + 10 - 130 = 0
x^2 + 7x - 120 = 0
(x-8)(x+15) = 0
x = 8 or x is a negative
the square was 8 by 8
To find the length of the side of the square, we need to solve the problem step by step:
Step 1: Understand the problem.
We are given a square. If its sides are extended, they form a rectangle. The extension on one side is 5 cm, and on the other side, it is 2 cm. The area of this rectangle is 130 cm^2.
Step 2: Set up the equation.
Let's assume the side of the square is "x" cm.
When one side is extended by 5 cm, the length of the rectangle becomes (x + 5) cm.
When the other side is extended by 2 cm, the width of the rectangle becomes (x + 2) cm.
The area of the rectangle is given by the formula: Area = length × width.
So, we have the equation: (x + 5) × (x + 2) = 130.
Step 3: Solve the equation.
Expanding the equation, we get:
x^2 + 7x + 10 = 130.
Rearranging the equation, we have:
x^2 + 7x - 120 = 0.
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Factoring the equation, we get:
(x + 15)(x - 8) = 0.
So, we have two possible solutions:
x + 15 = 0 → x = -15 (discard this solution since the side of a square cannot be negative).
x - 8 = 0 → x = 8.
Step 4: Check the solution.
Since the side of a square cannot be negative, we take x = 8 as our solution.
Therefore, the length of the side of the square is 8 cm.