In Fig. 6.21, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find PQ, QR and RS
Solution:
Given, PA, QB, RC and SD are all perpendicular to a line l.
Also, AB = 6 cm
BC = 9 cm
CD = 12 cm
SP = 36 cm
We have to find PQ, QR and RS.
From the figure, the lines PA, QB, RC and SD are parallel to each other.
The lines PA, QB, RC and SD are perpendicular to line l.
The Intercept theorem provides the ratios between the line segments created when two parallel lines are intercepted by two intersecting lines.
By Intercept theorem,
PQ/AB = QR/BC = RS/CD = PS/AD
AD = AB + BC + CD = 6 + 9 + 12 = 27 cm
So, PQ/6 = QR/9 = RS/12 = 36/27
Considering PQ/6 = 36/27
PQ/6 = 4/3
3PQ = 6(4)
PQ = 24/3
PQ = 8 cm
Considering QR/9 = 36/27
QR/9 = 4/3
On cross multiplication,
3QR = 9(4)
QR = 36/3
QR = 12 cm
Considering RS/12 = 36/27
RS/12 = 4/3
On cross multiplication,
3RS = 12(4)
RS = 48/3
RS = 16 cm
Therefore, the lengths of PQ, QR and RS are 8 cm, 12 cm and 16 cm respectively.
✦ Try This: In the figure seg PA, seg QB, seg RC and seg SD are perpendicular to line AD. AB = 60, BC = 70, CD = 80 , PS = 280 then find PQ,QR and RS.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.4 Problem 14
In Fig. 6.21, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find PQ, QR and RS
Summary:
In Fig. 6.21, PA, QB, RC and SD are all perpendicular to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm, then PQ, QR and RS are 8 cm, 12 cm and 16 cm respectively
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