Question 130100


If we cut the rectangle in two equal halves along the diagonal, we basically have this triangle set up:


{{{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,-0.2,10),
locate(1,2,x)
)}}}

Since we can see that the triangle has legs of 7 and 10 with a hypotenuse of x, we can use Pythagoreans theorem to find the unknown side.



Pythagoreans theorem:


{{{a^2+b^2=c^2}}} where a and b are the legs of the triangle and c is the hypotenuse




{{{7^2+10^2=x^2}}}  Plug in a=7, b=10, and c=x. Now lets solve for x



{{{4 9 + 1 0 0 =  x  ^ 2}}} Square each individual term




{{{1 4 9 =  x  ^ 2}}} Combine like terms



{{{s q r t ( 1 4 9 ) = s q r t (  x  ^ 2 )}}} Take the square root of both sides



Which approximates to...


{{{12.2065556157337=x}}}


So our answer is

{{{x=12.2065556157337}}}