sat suite question viewer

Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Hard

The figure presents right triangle A B C . Side A C is horizontal, vertex C is to the right of vertex A, vertex B is above side A C , and angle A B C is a right angle. Point D lies on side A C, directly below vertex B, and vertical line segment B D is drawn, dividing triangle A B C into two smaller triangles, triangle A B D and triangle B D C. Angle A D B is a right angle. A note states that the figure is not drawn to scale.

In the figure above, $the length of line segment B D equals 6$ and $the length of line segment A D equals 8$ . What is the length of $line segment D C$ ?

Back question 49 of 79 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

Explanation

The correct answer is 4.5. According to the properties of right triangles, BD divides triangle ABC into two similar triangles, ABD and BCD. The corresponding sides of ABD and BCD are proportional, so the ratio of BD to AD is the same as the ratio of DC to BD. Expressing this information as a proportion gives $six eighths equals, the fraction D C, over 6$ . Solving the proportion for DC results in $D C equals 4 point 5$ . Note that 4.5 and 9/2 are examples of ways to enter a correct answer.