Use the distributive property to write an equivalent expression for 13(4+13)

52+169

Step-by-step explanation:

First you multiply the 13, on the outside, with the 4.

Then you multiply the 13 with the other 13.

13*4=52

13*13=169

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