Question 764753

given:

The length of a rectangle  is {{{6cm}}} {{{less}}} than {{{twice}}} its width:

then we have {{{length +6cm=2*width}}}........eq.1

the perimeter of the rectangle is {{{30cm}}}:

{{{P=2*length+2*width}}}

if {{{P=30cm}}}, then {{{2*length+2*width=30cm}}} .....eq.2

now substitute {{{2*width}}} from eq.1 in eq.2

{{{2*length+(length +6cm)=30cm}}}......solve for {{{length}}}

{{{3*length =30cm-6cm}}}

{{{3*length =24cm}}}

{{{length =24cm/3}}}

{{{highlight(length =8cm)}}}

now go back to eq.1 and find the {{{width}}}


{{{length +6cm=2*width}}}........eq.1......plug in {{{length}}}

{{{8cm+6cm=2*width}}}

{{{14cm=2*width}}}

{{{width=14cm/2}}}

{{{highlight(width=7cm)}}}

so, your answer is C. {{{length= 8cm}}}; {{{width= 7cm}}}