Die diagram hieronder toon \( \triangle PQR \) met \( ST \parallel QR \) - NSC Technical Mathematics - Question 9 - 2023 - Paper 2
Question 9
Die diagram hieronder toon \( \triangle PQR \) met \( ST \parallel QR \).
\( PS = 8 \: cm, SQ = 3 \: cm \) en \( QR = 21 \: cm. \)
1. Gee die korrekte rede vir die... show full transcript
Worked Solution & Example Answer:Die diagram hieronder toon \( \triangle PQR \) met \( ST \parallel QR \) - NSC Technical Mathematics - Question 9 - 2023 - Paper 2
Step 1
Gee die korrekte rede vir die bewering:
PT = TR of...
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Answer
Die rede vir die bewering is dat die segmente in ( \triangle PQR ) in verhouding staan omdat die lynsegment ( ST ) parallel is aan ( QR ). Dit gevolg deur die basis hoeke se eienskappe van parallelle lyn. Daarom, ( PT:TR = PS:SQ ).
Step 2
Bereken vervolgens die lengte van PT.
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Answer
Die verhouding is gegee as ( PS:SQ = 8:3 ). Laat ( PT = x ) en ( TR = y ). Aangesien die totale lengte van ( QR = 21 : cm ) het jy die vergelyking ( x + y = 21 ).
As ( \frac{PT}{TR} = \frac{PS}{SQ} ):
[ \frac{x}{y} = \frac{8}{3} ]
Dus kan ons ( y ) uitdruk as ( y = \frac{3}{8}x ). Substituer dit in die eerste vergelyking:
[ x + \frac{3}{8}x = 21 ]
Hieruit resulterend in:
[ \frac{11}{8}x = 21 ]
Dus,
[ x = \frac{21 \times 8}{11} \approx 15.27 : cm. ]
Dus: ( PT \approx 15.27 : cm. )
Step 3
Voltooi die bewering en gee die korrekte rede:
ST = QR of...
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Answer
Aangesien ( ST \parallel QR ), is die verhouding van die lengtes van die lynsegmente: ( \frac{ST}{QR} = \frac{PS}{SQ}. )
