36. In the following figure, ST || QR, point S divides PQ in the ratio 4:5. If ST = 1.6 cm, what is the length of QR?
Answers
Answer:
The Answer is 3.6 (c)
Step-by-step explanation:
As S divides PQ in the ratio 4:5
Then, PS:SQ = 4:5
PS/SQ + PS = 4:9
PS/PQ = ST/QR (As triangle(PST) is similar to triangle(PQR) )
4/9 = 1.6/x
x = 3.6
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Length of QR is 3.6 cm if ST || QR, S divides PQ in the ratio 4:5 and ST = 1.6 cm
Given:
- ST || QR
- S divides PQ in the ratio 4:5
- ST = 1.6 cm
To Find:
- Length of QR
Solution:
Corresponding angles : A pair of angles that occupy the same relative position at each intersection by a transversal line
Corresponding angles formed by transversal line with two parallel lines are congruent. ( Equal in Measure)
Step 1:
Show that ΔPST and ΔPQR are similar using AAA Similarity
∠P = ∠P Common
∠S = ∠Q ( corresponding angles)
∠T = ∠R ( corresponding angles)
=> ΔPST ~ ΔPQR
Step 2:
Corresponding sides of similar triangle are in proportion hence
ST/QR = PS/PQ
Step 3:
Use PQ = PS + SQ and ST = 1.6 and solve for QT
1.6/QR = PS/(PS + SQ)
=>QR = 1.6(PS + SQ)/PS
=>QR = 1.6 + 1.6 * SQ/PS
Step 4:
Substitute SQ./PS = 5/4 as PS : SQ = 4 : 5 and find value of QR
QR = 1.6 + 1.6 * (5/4)
=> QR = 1.6 + 2
=> QR = 3.6 cm
Length of QR is 3.6 cm
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