Question

a plot of land is in the shape of a square. the shaded square inside is covered with gravel. the rest of the square plot is covered in grass. its area is 1400 square feet. how long are the sides of the square?

Explanation:

Step1: Set up the equation

The area of the large square is \(x^{2}\) (since area of a square \(A = s^{2}\), where \(s=x\)). The area of the gravel - covered square is \(200\) square feet. The area of the grass - covered part is \(1400\) square feet. So, \(x^{2}-200 = 1400\).

Step2: Solve for \(x^{2}\)

Add \(200\) to both sides of the equation \(x^{2}-200 = 1400\). We get \(x^{2}=1400 + 200\). So, \(x^{2}=1600\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a square (\(x>0\)), \(x=\sqrt{1600}\). And \(\sqrt{1600}=40\).

Answer:

The sides of the square are \(40\) feet long.