Find the perimeter of a rectangle that is 7 cm longer than wide and has an area of 120 cm ^ 2.

Width b cm;
Length a = b + 7 cm;
Area S = 120 cm ^ 2;
Perimeter P -?;
Apply the formula for the area of a rectangle: S = ab.
Substitute the area value, length and width expressions into this formula.
120 = (b + 7) b;
We open the brackets on the right side of the equation according to the distribution law of multiplication.
120 = b ^ 2 + 7b;
We transfer the terms of the equation from the left to the right, while changing the sign of each term to the opposite.
-b ^ 2-7b + 120 = 0;
Multiply the left and right sides by -1.
b ^ 2 + 7b-120 = 0;
By Vieta’s theorem.
b1 = -15; – width cannot be negative.
b2 = 8;
b = 8 (cm);
a = 8 + 7 = 15 (cm);
P = 2 (a + b) = 2 (15 + 8) = 46 (cm).