Question

A plot of land doubles in size by adding x meters to the length and x meters to the width of the land. If the original plot had an area of 200 by 300 meters, what is the value of x?

Answer 1

Given:
plot of land doubles in size.
original plot area 200 by 300 meters

Area = 200m * 300m
A = 60,000 m²  original plot area

60,000m² x 2 = 120,000 m²

(200m + x)(300m + x) = 120,000 m²

60,000m² + 200m*x + 300m * x + x² = 120,000 m²

x² + 500x + 60,000 = 120,000
x² + 500x + 60,000 - 120,000 = 0
x² + 500x - 60,000 = 0

x = -b + (√b² - 4ac)/2a 

a = 1 ; b = 500 ; c = -60,000

x = -500 + (√500² - 4(1)(-60,000)) / 2(1)
x = (-500 + (√250,000 + 240,000)) / 2 
x = (-500 + 700)/ 2
x = 200 / 2
x = 100 meters

(200 + x)(300 + x) = 120,000
(200 + 100)(300 + 100) = 120,000
300 * 400 = 120,000
120,000 = 120,000