Question

In a rectangle, the length is twice the width. The diagonal of the rectangle is the square of the width. Find the are of the rectangle.

Answer 1

Area= L*W
L= 2W (L is twice the width)
so, Area= 2W^2

Also, we know the diagonal D= W^2. But by the pythagorean theorem, D^2= L^2 + W^2

so L^2 + W^2=W^4

substitute for L=2W to get
4W^2+W^2= W^4
divide by W^2 to get
4+1= W^2
or W^2 =5
remember that Area= 2W^2 (see above)
or Area= 2*5=10