Examples with solutions for Difference of squares: Worded problems

Exercise #1

The length of the side of the square x+1 x+1 cm

(x>3)

We extend one side by 1 cm and shorten an adjacent side by 1 cm, and we obtain a rectangle.

What is the area of the rectangle?

Video Solution

Answer

x2+2x x^2+2x

Exercise #2

The length of the square is equal to x x cm

(x>1) We extend one side by 3 cm and shorten an adjacent side by 1 cm and we obtain a rectangle,

What is the length of the side of the given square if it is known that the two areas are equal?

Video Solution

Answer

x=32cm x=\frac{3}{2}cm

Exercise #3

The length of the side of a square is X cm

(x>3)

Extend one side by 3 cm and shorten an adjacent side by 3 cm to obtain a rectangle.

Express the area of the rectangle using x.

Video Solution

Answer

x29(cm2) x^2-9\left(\operatorname{cm}²\right)

Exercise #4

The side length of a square is X cm

(x>3)

We extend one side by 3 cm and shorten an adjacent side by 3 cm, and we get a rectangle.

Which shape has a larger area?

Video Solution

Answer

The square