Question 951465


A rectangle with diagonals of length {{{d=20cm}}} has sides in the ratio {{{2 : 1}}}. 

diagonal divide a rectangle in two right-angle triangles

so, if sides of a rectangle are {{{a}}} and {{{b}}} then we can write equation
{{{d^2=a^2+b^2}}}

since  {{{d=20cm}}}, we have


{{{(20cm)^2=a^2+b^2}}}

{{{400cm^2=a^2+b^2}}}

since  sides in the ratio {{{2 : 1}}}, we have

{{{a:b=2 : 1}}} =>{{{a=2b}}}..substitute in eq. above

{{{400cm^2=(2b)^2+b^2}}}.......solve for {{{b}}}

{{{400cm^2=4b^2+b^2}}}

{{{400cm^2=5b^2}}}

{{{400cm^2/5=b^2}}}

{{{80cm^2=b^2}}}

{{{b=sqrt(80cm^2)}}}

{{{b=8.94cm}}}

{{{a=2b}}}=>{{{a=2*8.94cm}}}=>{{{a=17.88cm}}}


Find the:

a) perimeter

{{{P=2a+2b}}}

{{{P=2*17.88cm+2*8.94cm}}}

{{{P=2*17.88cm+2*8.944271909999159cm}}}

{{{P=35.76cm+17.88cm}}}

{{{P=53.64cm}}}

b) area of the rectangle. 

{{{A=ab}}}

{{{A=17.88cm*8.94cm}}}

{{{A=159.8472cm^2}}}