Question 107935
The diagonal divides the rectangle into 2 equal right triangles.
Let the diagonal=c and the 2 sides be a and b.
a=c-2, b=c-5
a^2+b^2=c^2
(c-2)^2+(c-5)^2=c^2
c^2-4c+4+c^2-10c+25=c^2
c^2-14c+29=0
c^2-14c   =-29
c^2-14c+49=49-29 complete the square
(c-7)^2=20
c-7=+-sqrt(20)
c=7+-sqrt(5*4)
=7+-2sqrt(5)
Only 7+2sqrt(5) is the only correct answer for the diagonal. the other would lead to negative numbers for the sides of the rectangle.
The sides of the rectangle are:
5+2sqrt(5) and 2+2sqrt(5)
Ed