If bc = 6 and ad = 5, find dc. a) 4 b) 4.5 c) 7.2

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

4

1 and 2

step-by-step explanation:

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

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