The area of the rectangle is 675 cm². find the side of a rectangle if one of them is 30 cm smaller than the other

To solve this problem, you need to write an equation. Let’s recall the formula for the area of ​​a rectangle. The area of ​​the rectangle is equal to the product of the length and the width. S = a * b, where a is the length and b is the width. Let the width be – x cm, then the length – (x + 30) cm. Knowing the area of ​​the rectangle is 675 cm ^ 2, we will compose the equation.
x * (x + 30) = 675
x ^ 2 + 30x-675 = 0;
We got a quadratic equation, we calculate the discriminant.
a = 1; b = 30; c = -675.
D = b ^ 2-4ac = 900 + 4 * 675 = 900 + 2700 = 3600;
x = -b + vD / 2a = -30 + 60/2 = 15;
x = -b-vD / 2a = -30-60 / 2 = -90 / 2 = -45.
We got two answers -45 and 15, since the side of the rectangle cannot be negative, then the width is 15 cm, and the length is 15 + 30 = 45 cm. Let’s check. S = 15 * 45 = 675 cm ^ 2. Answer: 15 cm, 45 cm.