When pascal built a dog house, he knew he wanted the floor of the house to have an area of 24 square feet. he also wanted the width to be 2/3 the length. what are the dimensions of the dog house?

so, converting firstly the mixed fractions to improper fractions and then "adding".

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