ABCD is a rectangular sheet of paper that has been folded so that corner B is matched with point B' on edge AD. The crease is EF, where E is on AB and F is on CD. The dimensions AE=8, BE=12, and CF=2 are given. Find the perimeter of recangle ABCD.
+2668 Note thatBE=B′E=12
By the Pythagorean Theorem, AB′=√B′E2−AE2=√144−64=√80=4√5
Also, note that by the Pythagorean Theorem, B′F=DF2+B′D2=CF2+BC2
SImplifying the equation gives us: 4+BC2=324+B′D2
But, note that B′D=BC−AB′=BC−4√5
This means that our equation simplifies to 4+BC2=324+(BC−4√5)2
Now, just solve for BC, and I assume you can take it from here?
+2668 Note thatBE=B′E=12
By the Pythagorean Theorem, AB′=√B′E2−AE2=√144−64=√80=4√5
Also, note that by the Pythagorean Theorem, B′F=DF2+B′D2=CF2+BC2
SImplifying the equation gives us: 4+BC2=324+B′D2
But, note that B′D=BC−AB′=BC−4√5
This means that our equation simplifies to 4+BC2=324+(BC−4√5)2
Now, just solve for BC, and I assume you can take it from here?
