-
kamalakarthi
- Senior | Next Rank: 100 Posts
- Posts: 80
- Joined: Mon Jan 31, 2011 10:08 pm
- Followed by:2 members
First, note that triangle ABD is a 3:4:5 triangle. If the two sides are 6 and 8, then the hypotenuse, or AD, is 10. If AD = 10, and ED = 5, then AE is also 5, Now we have the following figure.kamalakarthi wrote:Can you help me with the below.
Next, we can see that triangles ABD and ECD are similar. They each have a 90 degree angle, and they share angle EDC. If all the angle measurements of two triangles are the same, the triangles must have sides in the same proportion, so triangle ECD is also a 3:4:5. if ED = 5, then EC = 3 and CD = 4. Now we have the following:
Because FC = 6, and EC = 3, FC must also be 3. Now we can see that triangle AFE is also a 3:4:5 and AF is 4. So now we have:
Last, we can find the area of the shape ABCE by taking the area of rectangle ABCF and subtracting the area of triangle AFE.
Area rectangle ABCF = 6*4 = 24
Area triangle AFE = 3*4/2 = 6
Difference: 24-6 = 18. Answer is B
