The most common problems involving quadratic equations are finding the dimensions when the area is given.
Example:
Find the dimensions of a rectangular textbook whose length is 10cm longer than its width and covers an area of 375 cm².
Solution:
Let x be the width of the textbook
x+10 be the length of the textbook
A = width·length
375 = x (x+10)
375 = x² +10x
0 = x² +10x -375
0 = (x+25) (x-15)
x+25 = 0 ; x-15 = 0
x = -25 ; x = 15 (use x=15 because dimensions may never be negative)
Answer :
Width = 15 cm
Length = 25 cm (from x+10)
