Square ABCD and rectangle ACEG have the same area. Find the ratio AC:CE Please explain how you got the answer. Thanks!

2

Step-by-step explanation:

Ok, so let us assume that AB = x, from here we know the length of AC is xsqrt(2).

So,

area of ABCD = area of ACEG = x^2

From here, AG = x^2/xsqrt(2), which equals xsqrt(2)/2

Finally, AC to CE = xsqrt(2) : xsqrt(2)/2

which is 2/1

1

step-by-step explanation:

you are throwing one dart

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4