Die diagram hieronder toon ΔPQR met ST ∥ QR - NSC Technical Mathematics - Question 9 - 2023 - Paper 2
Question 9
Die diagram hieronder toon ΔPQR met ST ∥ QR.
PS = 8 cm, SQ = 3 cm, RT = 4 cm en QR = 21 cm.
9.1 Gee die korrekte rede vir die bewearing: PT/TR = PS/SQ (...)
9.2 B... show full transcript
Worked Solution & Example Answer:Die diagram hieronder toon ΔPQR met ST ∥ QR - NSC Technical Mathematics - Question 9 - 2023 - Paper 2
Step 1
9.1 Gee die korrekte rede vir die bewearing: PT/TR = PS/SQ (...)
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Die rede vir die bewaring is dat die ooreenstemmende syfer van gelyke driehoeke gelyke verhouding het. Aangesien ST parallel is aan QR, het ons dat die hoeke van ΔPST en ΔPQR gelyk is, wat impliseer dat die syfers in verhouding is.
Step 2
9.2 Bereken vervolgens die lengte van PT.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Die verhouding is: PT/TR = PS/SQ.
Hier, PS = 8 cm en SQ = 3 cm. Ons weet ook dat QR = 21 cm, wat beteken dat TR = QR - RT = 21 cm - 4 cm = 17 cm.
Dus, PT = (PS/SQ) * TR = (8/3) * 17 = 45.33 cm.
Dus, PT = 15.33 cm.
Step 3
9.3 Voltooi die bewaring en gee die korrekte rede: ST/QR = PS/SQ.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Hier is die bewaring: ST/QR = PS/SQ.
Grafiek wys dat ST parallel met QR is, so met behulp van die gelyke verhouding kan ons hierdie bewaring bevestig.
Step 4
9.4 Bereken vervolgens die lengte van ST.
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Aangesien ons weet dat ST/QR = PS/SQ, kan ons die lengte van ST bereken.
