The area of a rectangular plate is 120 cm. Find the perimeter of this plate if it is known that the

The area of a rectangular plate is 120 cm. Find the perimeter of this plate if it is known that the length is 2 cm greater than the width.

The task
Plate area S – 120 square centimeters
Perimeter P -? centimeters
Length a -? , 2 centimeters wider
Width b -?
Solution
1) Let’s compose two equations
a b = 120
a = b + 2
2) Substitute the value a into the first equation and determine the width of the plate
(b + 2) b = 120
b ^ 2 + 2 b – 120 = 0 – quadratic equation
D = 2 ^ 2 – 4 1 (-120) = 4 + 480 = 484
b1 = (-2 + v 484) / 2 = (-2 + 22) / 2 = 10 (cm) – width
b2 = (-2 – v 484) / 2 = -24/2 = – 12 <0
3) Calculate the length of the plate
a = b + 2 = 10 + 2 = 12 (cm)
4) Find the perimeter of the plate
P = (a + b) 2 = (12 + 10) 2 = 22 2 = 44 (cm)
Answer: P = 44 centimeters