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QUESTION 9 The diagram below is a picture of a triangular roof truss, as shown - NSC Technical Mathematics - Question 9 - 2021 - Paper 2
Question 9
QUESTION 9 The diagram below is a picture of a triangular roof truss, as shown. Triangle ABC has AB = AC. DE || BC and F is the midpoint of BC. AE : EC = 1 : 2 and ... show full transcript
Worked Solution & Example Answer:QUESTION 9 The diagram below is a picture of a triangular roof truss, as shown - NSC Technical Mathematics - Question 9 - 2021 - Paper 2
Step 1
9.1.1 DB, giving reason(s)
Answer
To determine the length of DB, we use the property of triangles that states:
Since AB = 1.8 m and EA : EC = 1 : 2, we can derive:
Let EC = 2x and EA = x.
Then, [
EA + EC = 1.8
\Rightarrow x + 2x = 1.8
\Rightarrow 3x = 1.8
\Rightarrow x = 0.6
\Rightarrow EC = 2(0.6) = 1.2
]
Hence, since DB = \frac{1}{2} AB, we have:
Step 2
9.1.2 DF if DF = \frac{3}{2} AD
Answer
Using the relationship indicated, we know that DF is a fraction of AD:
Given the lengths: AB = 1.8 m and AE = 0.6 m (from previous calculation), we have:
Using the triangle similarity, FC = 0.9 m (as F is the midpoint). Thus, AD can be computed as:
AD = AB - EA = 1.8 - 0.6 = 1.2 m.\
Now calculating DF:
Step 3
9.2 Determine, giving reasons, whether EF is parallel to AB.
Answer
To determine if EF is parallel to AB, we consider the fact that EF is drawn between points that are midpoints of the sides of triangle ABC.
Given:
- BF = FC; F is the midpoint of BC
- AE = EC
Since DE || BC, it implies that the ratio of segments along AB and AC must remain the same proportion. This relationship shows that EF is NOT parallel to AB, as the segments do not maintain equal proportions in the triangle geometry.
Thus, we conclude:
Conclusion
EF is NOT parallel to AB.