Question

The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. Find the side of the square, if it’s known that the area of the square is 30 cm2 less than the area of the rectangle.

Quickly 10 points

Answer 1

`a-the\ side\ of\ square\\a^2-the\ area\ of\ square\\\\a+3-the\ one\ side\ of\ rectangle\\a-2-the\ second\ side\ of\ rectangle\\(a+3)(a-2)-the\ area\ of\ rectangle\\\\\text{The equation:}\\\\(a+3)(a-2)=a^2+30\qquad\text{use distributive property}\\\\(a)(a)+(a)(-2)+(3)(a)+(3)(-2)=a^2+30\\\\a^2-2a+3a-6=a^2+30\qquad\text{subtract}\ a^2\ \text{from both sides}\\\\a-6=30\qquad\text{add 6 to both sides}\\\\\boxed{a=36}\\\\Answer:\ \boxed{36\ cm}`