Question

if we increased one side of a square by 3 units and decreased the other side by 4 units, the area of the resulting rectangle would be 20 unit² less than the area of the square. how long are the sides of the original square?
answer:
units
question help: video

Explanation:

Step1: Let side - length of square be \(x\)

Let the side - length of the original square be \(x\) units. Then the area of the square is \(A_{square}=x^{2}\) square units.
The new rectangle has sides \((x + 3)\) units and \((x-4)\) units, and its area is \(A_{rectangle}=(x + 3)(x - 4)\) square units.

Step2: Set up the equation

We know that the area of the resulting rectangle is 20 square units less than the area of the square. So, \((x + 3)(x - 4)=x^{2}-20\).
Expand the left - hand side using the FOIL method: \(x^{2}-4x+3x - 12=x^{2}-20\).

Step3: Simplify the equation

Combine like terms on the left - hand side: \(x^{2}-x - 12=x^{2}-20\).
Subtract \(x^{2}\) from both sides of the equation: \(-x-12=-20\).

Step4: Solve for \(x\)

Add 12 to both sides: \(-x=-20 + 12\), so \(-x=-8\).
Multiply both sides by \(-1\) to get \(x = 8\).

Answer:

8