Find AC in the Rectangle

Question

In rectangle ABCD, AB= x+15, BC= x-8, and CD = 2x+3. Find AC to the nearest hundredth.

Answer 1

In a rectangle, opposite sides are congruent so we know AB=CD

Set those equations equal to solve for x

x+15=2x+3; solve for x which gives us x=12

plug in to AB and BC, which gives ust AB=27 and BC = 4

We want the diagonal which is AC. ABC for a right triangle so we use the Pythagorean theorem to solve for AC.

27^2 + 4^2=AC^2

729+16

745=AC^2

Take the square root of both sides which gives us 27.29