Abbie collects 5p coins. on tuesday she adds 7 more coins to her collection. how much money did abbie add on tuesday?

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

you have 6 equal triangles, find the area of one of them (b*h/2) and multiply by 6

(8*4: 2)*6 =

32 cm² is your answer