Problema Solution
a triangle has base 12 centimeters and height 8 centimeters. how much do you have to increase each dimension equally so that the area is tripled?
Answer provided by our tutors
I presume 8 is the height
area = 1/2 * 12 * 8
area = 48 cm^2
thrice = 48*3=144 cm^2
increase both by x
area after increase = 1/2 * (12+x)(8+x)
area = 1/2 * ( 96+12x+8x+x^2) by FOIL
area = 1/2 * (x^2+20x+96)
144= 1/2 ( (x^2+20x+96)
288=x^2+20x+196
x^2+20x-192=0
Find the roots of the equation by quadratic formula
a= 1 b= 20 c= -192
b^2-4ac= 400 + 768
b^2-4ac= 1168
= 34.18
x1=( -20 + 34.18 )/ 2
x1= 7.09
x2=( -20 -34.18 ) / 2
x2= -27.09
Ignore negative value
increase by 7.09 cm