Question

Look at the figure below: Triangle ABC is a right triangle with angle ABC equal to 90 degrees. The length of AC is 7 units, and the length of AB is 4 units. D is a point above C. Triangle ADC is a right triangle with angle DAC equal to 90 degrees and DC parallel to AB. What is the length, in units, of segment CD? 5.50 12.25 8 14

Answer 1

The length of AB determined using SSS similarity theorem is 8.

The provided triangles are right angle triangles and are similar triangles based on side-side-side (SSS) similarity theorem.

According to SSS similarity theorem, if all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

As the triangles are similar, the ratio between the hypotenuses and bases of the two triangles are equal.

Using the SSS similarity theorem of triangle,

AC/AD = AB/AE

Based on the figure,

AC = AB + BC = AB + 12

AD = 15

AB = AB = ?

AE = AD – ED = 15 – 9 = 6

Substituting the values,

(AB + 12)/15 = AB/6

6(AB + 12) = 15AB

6AB + 72 = 15AB

15AB – 6AB = 72

9AB = 72

AB = 8