Emma is building a scale model of a jet airplane. The real airplane has a wingspan of 200 feet and a length of 240 feet. If Emma’s model has a wingspan of 30 centimeters, what is the length of the model ?

Since it is a to-scale model,

the ratio of the wingspan to the length of both the airplanes must be equal

wingspan1 = 200 ft               wingspan2 = 30 cm

length1 = 240 ft                     length2 = x cm

wingspan1 / length1 = wingspan2/length2

replacing the variables

200 / 240 = 30 / x

x = 30 * 240/200

x = 36 cm

Therefore, the length of Emma's airplane is 36 cm

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

a

step-by-step explanation: