Question 923837

A right-angled triangle has an area of {{{30cm^2}}}:

{{{A=(width*height)/2}}} => {{{(width*height)/2=30cm^2}}}

if the width of the triangle is {{{W=n+3cm}}}, and the height {{{h}}} is {{{4cm}}} less than the width, then we have

{{{W=n+3cm}}}
{{{h=n+3cm-4cm}}}=>{{{h=n-1cm}}}

go to {{{(width*height)/2=30}}}, plug in {{{W=n+3cm}}} and {{{h=n-1cm}}}

{{{((n+3)*(n-1))/2=30cm^2}}}

 {{{(n+3cm)*(n-1cm)=60cm^2}}}

{{{n^2-n*cm+3n*cm-3cm^2=60}}}

{{{n^2+2n*cm-3cm^2-60cm^2=0}}}

{{{n^2+2n*cm-63cm^2=0}}}.........write {{{2n*cm}}} as {{{9n*cm-7n*cm}}}

{{{n^2+9n*cm-7n*cm-63cm^2 = 0}}}...group

{{{(n^2+9n*cm)-(7n*cm+63cm^2) = 0}}}..factor

{{{n(n+9cm)-7cm(n+9cm) = 0}}}

{{{(n-7cm)(n+9cm) = 0}}}

we need only positive solution and it is {{{n-7cm = 0}}}=>{{{highlight(n=7cm)}}}

now find 

{{{width=n+3cm}}}=>{{{width=7cm+3cm}}}=>{{{width=10cm}}}
{{{height=n-1cm}}}=>{{{h=7cm-1cm}}}=>{{{h=6cm}}}