Question

CDEF is a rectangle with a width of 3 and a length of 4. One diagonal is 3x - 2y and the other diagonal is 8x + 3y. Find the values of x and y.

Answer 1

3x-2y=5
8x+3y=5

x=1
y=-1

Answer 2

x = 1 y = -1

Answer 3

but do we know why the diagonal is 5?

Answer 4

Because it's a Pythagorean triple. 3,4,5 is a pretty simple one, and there are a few other easy ones like that. \[a ^{2} + b ^{2} = c ^{2}\] Simple rule of thumb: if you have a right triangle, and the smallest side is odd, the other side and hypotenuse will be two consecutive numbers that add up to the square of the smallest number.

Answer 5

:-) I know you knew that