Triangles ABC and DEC are similar. Side DE is 1.2 feet, side EC is 2 feet, and side BE is 0.3 foot.

Question

right triangle ABC with segment DE drawn so that point D is on side AC and point E is on side BC, creating right triangle DEC

Part A: Describe how to draw triangles ABC and DEC separately. Be sure to give the lengths of sides BC, DE, and EC in the description. (6 points)

Part B: Find side AB. Show each step of your work. (6 points)
(dumb it down a lot and make it seem like an 8th grader wrote it in 3 sentences)

Answer 1

Part A:
To draw triangle ABC, start by sketching a right triangle. Make side BC 0.3 feet long, then draw side AC perpendicular to BC. Now, draw side AB connecting point B to point A. Next, for triangle DEC, make side DE 1.2 feet long and side EC 2 feet long. Place point D on side AC and point E on side BC, ensuring triangle DEC is similar to triangle ABC.

Part B:
Since triangles ABC and DEC are similar, we can set up a ratio using the sides we know. We have DE and EC for triangle DEC, which are 1.2 feet and 2 feet, respectively. The corresponding sides in triangle ABC are AB and BC (0.3 feet).

So, we can set up the ratio like this:
\[ \frac{AB}{BC} = \frac{DE}{EC} \]
Which means:
\[ \frac{AB}{0.3} = \frac{1.2}{2} \]

Now, simplify \(\frac{1.2}{2}\) to get \(0.6\):
\[ \frac{AB}{0.3} = 0.6 \]

Next, to find AB, multiply both sides by 0.3:
\[ AB = 0.6 \times 0.3 = 0.18 \]

So, AB is 0.18 feet!