Question 391126
let x =number of cm each side of the rectangle was increased
area of rectangle = length * width
length of new rectangle = (x+6)cm
width of new rectangle = (x+4)cm
given area of new triangle =39 cm^2

(x+6)(x+4)=39
x^2+10x+24=39
x^2+10x-15=0
use the following quadratic formula to solve for x
with a =1,b=10,c=-15

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

x=((-10)ħsqrt(10^2-4*1*(-15))/2*1
   = ((-10)ħsqrt(100+60)=-10ħsqrt(160))2
    
=(-10ħ12.65)/2=2.65/2 or -22.65/2
=1.33 or -11.33(reject)

ans: each side of the rectangle was increased by 1.33 cm

check: 7.33*5.33=39.07 (approximate because of rounding to two decimal places)