Question 195281
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1) Area of Triangle = (1/2)base x height



Substituting given:
{{{12cm^2=(1/2)(x)(x+2)}}}
Cross multiply/ expand:
{{{12*2=x*2+2x}}}
Combine all terms:
{{{x^2+2x-24=0}}}
{{{(x+6)(x-4)=0}}}
{{{x=-6}}}, disregard
{{{highlight(red(x=4cm))}}}, base
Also, {{{4+2=highlight(red(6cm))}}}, height


Check,
{{{12cm^2=(1/2)(4)(6)}}}
{{{12cm^2=(1/2)24cm^2}}}
{{{12cm^2=12cm^2}}}



2) Area of Rectangle = Length x Width


Substitue given:
{{{160ft^2=(x)(x-12)}}}
{{{160=x^2-12x}}}
{{{x^2-12x-160=0}}}
{{{(x+8)(x-20)=0}}}
{{{x=-8}}}, disregard "-"
{{{highlight(red(x=20ft))}}}, Length
Also, {{{20-12=highlight(red(8ft))}}}, Width


Check,
{{{160ft^2=20*8}}}
{{{160ft^2=160ft^2}}}