Question 177147


If we divide the rectangle in half along the diagonal, we get the following triangle:



{{{drawing(500,500,-0.5,2,-0.5,3.2,
line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,7),
locate(1,-0.2,12),
locate(1,2,x)
)}}}



Since the legs are {{{7}}} and {{{12}}} this means that {{{a=7}}} and {{{b=12}}}


   

Also, since the hypotenuse is {{{x}}}, this means that {{{c=x}}}.



{{{a^2+b^2=c^2}}} Start with the Pythagorean theorem.



{{{7^2+12^2=x^2}}} Plug in {{{a=7}}}, {{{b=12}}}, {{{c=x}}} 



{{{49+12^2=x^2}}} Square {{{7}}} to get {{{49}}}.



{{{49+144=x^2}}} Square {{{12}}} to get {{{144}}}.



{{{193=x^2}}} Combine like terms.



{{{x^2=193}}} Rearrange the equation.



{{{x=sqrt(193)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



{{{x=13.892}}} Approximate the square root with a calculator.



{{{x=13.9}}} Round to the nearest tenth.



================================================================



Answer:



So the length of the diagonal is approximately 13.9 units.