Question 659094
"A triangle has an area of 10 cm2.   The height of the triangle is 4 cm longer than three times the base.   Find the height and base of the triangle."

A=10cm2
h=4+3b

find h and b


A=1/2(bh)
10cm2=[b(4+3b)]/2

20cm2=4b+3b2

3b2+4b-20=0

using quadratic equation:


a=3  ;  b=4 ; c=-20

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

{{{base=(-4+-sqrt(4^2-4*3*-20))/(2*3)}}}

base1=2

base2=-3.333


we will take base 1 because it  is positive

h=4+3b

h=4+3(2)


h=10

checking:

A=1/2(bh)

A=1/2(2)(10)

10cm2=10cm2 (correct)

the base and height is 2cm and 10cm respectively.

i hope it helped you :)