Question 118667
If we cut the rectangle in half along the diagonal, we get this 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,x),
locate(1,-0.2,45),
locate(1,2,51)
)}}}


Since we can see that the triangle has legs of x and 45 with a hypotenuse of 51, 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




{{{x^2+45^2=51^2}}}  Plug in a=x, b=45, and c=51. Now lets solve for x



{{{ x  ^ 2 + 2 0 2 5 = 2 6 0 1}}} Square each individual term




{{{ x  ^ 2 = 2 6 0 1 - 2 0 2 5}}} Subtract 2025 from both sides



{{{ x  ^ 2 = 5 7 6}}} Combine like terms



{{{s q r t (  x  ^ 2 ) = s q r t ( 5 7 6 )}}} Take the square root of both sides




{{{x=24}}} Simplify the square root





So the width is 24



{{{A=24*45=1080}}} Now multiply 24 and 45 to get the area



So the area of the rectangle is 1080