By what number must 566 be divided so as to give a quotient 15 and a remainder 11? (with steps)

37

Step-by-step explanation:

we would had to call the number needed a random value or call it x but

let's do the calculation backward to ease things up

(566 - 11) ÷15 ➡ 555 ÷ 15 = 37

step-by-step explanation:

the shape,the size and the distance

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