Question

Shown here is a triangular striped sail, together with some of its dimensions. In the diagram, segments BJ, CI, and DH are all paralell to segment EG. Find each of the following.

1. AJ
2. CD
3.HG
4. GF
5. the perimeter of triangle AEF
6. the area of triangle AEF
7. the number of sails you could make for $10,000 if the sail costs $30 per square yard

Answer 1

Here, Just apply Proportionality Theorem at correct time, with correct proportions, It tells, the ratio of two corresponding arms always equal.

So, 1) AB/BC = AJ/JI
2.5/2.25 = AJ/1.8
AJ = 2.5* 1.8 / 2.25
AJ = 2

2) BC/CD = JI / IH
2.25/CD = 1.8/1.2
CD = 2.25 * 1.2 / 1.8
CD = 1.5

3) CD/DE = IH/HG
1.5/3.5 = 1.2 / HG
HG = 1.2 * 3.5 / 1.5
HG = 2.8

4) For GF, we should use "Pythagoras Theorem"
h² = a² + b²
GF² = 6.5² - 6²
GF² = 42.25 - 36
GF = √6.25
GF = 2.5

5) Perimeter = 2.5 + 2.25 + 1.5 + 3.5 + 6.5 + 2.5 + 2.8 + 1.2 + 1.8 + 2
P = 26.55

6) Area = 1/2 * b * h
A = 1/2 * 9.65 * 10.3
A = 49.70

Hope this helps!