Write each number as a product of a decimal number between 1 and 10 and a power of 10.
234,000

2.34 * 10^5.

Step-by-step explanation:

234000 = 2.34 * 10^5

- there are 5 digits after the first number so the exponent is 5.

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