The length of the rectangle is 12 cm. Its area is 36 cm ^ 2 larger than the area of a square

The length of the rectangle is 12 cm. Its area is 36 cm ^ 2 larger than the area of a square with a side equal to the width of the rectangle. Find the side of the square.

We introduce a variable and denote x cm – the width of the rectangle and, as stated by the condition, the side of the square.
Let’s write the areas of these figures:
S straight = a * b = 12 * x = 12x;
S square = a² = x².
It is known that the area of a rectangle is 36 cm² larger than the area of a square. We can make an equation:
12x – x² = 36
x² – 12x + 36 = 0
Find the discriminant and the roots of the quadratic equation:
D = b2 – 4ac = (-12) 2 – 4 1 36 = 144 – 144 = 0
The discriminant is zero, the equation has one root:
x = 12/2 = 6 (cm).
Answer: the side of the square is 6 centimeters.