Question

A rectangle is 24 cm long and 17 cm wide. When its length decreases by x cm and its breadth increases by x cm, its area is increased by 12cm ^ 2

(a) Express, in terms of x,

(i) the new length,
(ii) the new breadth,
(iii) the new area of the rectangle.

(b) Find the possible values of x.​

Answer 1

(i) the new length,= 24-x

(ii) the new range = 17+x

(iii) the new area of the rectangle=(24-x)(17+x)=-x²+7x+408

(b) Find the possible values of x.​

-x²+7x+408 = 24*17+12

-x²+7x+408 = 420

-x²+7x+408-420=0

-x²+7x-12=0

b²-4²c =7²-4(-1*-12)= 49-48=1

delta=1

(-b-Vdelta)/2a = (-7-1)/-2= 4

(-b+Vdelta)/2a=(-7+1)/-2=3

possible values of x: 4;3