Question 919552

The area of a triangle is:{{{A=(1/2)b*h}}}

given
 {{{A=34 cm^2}}}=> {{{(1/2)b*h=34cm^2}}}..........eq.1


 If the base of the triangle is increased by {{{5cm}}}, the area of the triangle would be {{{51cm^2}}}.
 
{{{(1/2)(b+5cm)*h=51cm^2}}}..........eq.2

How long is the base of the triangle?

solve the system: 

{{{(1/2)b*h=34cm^2}}}..........eq.1

{{{(1/2)(b+5cm)*h=51cm^2}}}..........eq.2
_________________________________________subtract 1 from 2

{{{(1/2)(b+5cm)*h-(1/2)b*h=51cm^2-34cm^2}}}

{{{(1/2)((b+5cm)*h-b*h)=17cm^2}}}

{{{cross(b*h)+5cm*h-cross(b*h)=2*17cm^2}}}

{{{5cm*h=34cm^2}}}

{{{h=34cm^2/5cm}}}

{{{h=6.8cm}}}

go to eq.1 and plug in {{{6.8cm}}} for {{{h}}}

{{{(1/2)b*6.8cm=34cm^2}}}..........eq.1.....solve for {{{b}}}

{{{(1/cross(2))b*cross(6.8)3.4cm=34cm^2}}}

{{{b*3.4cm=34cm^2}}}

{{{b=34cm^2/3.4cm}}}

{{{b=340cm^2/34cm}}}

{{{highlight(b=10cm)}}} ...the base of the triangle