In Fig. 9.21, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is
a. 6 cm
b. 9 cm
c. 4 cm
d. 2 cm
Solution:
It is given that
PR = 12 cm
QR = 6 cm
PL = 8 cm
In right angled triangle PLR
Using the Pythagoras theorem
PR² = PL² + LR²
LR² = PR² - PL²
Substituting the values
LR² = 144 - 64
LR² = 80
LR = √80 = 4√5 cm
Here
LR = LQ + QR
LQ = LR - QR
Substituting the values
LQ = 4√5 - 6 cm
Area of triangle PLR
A1 = 1/2 × LR × PL
Substituting the values
A1 = 1/2 × 4√5 × 8 = 16√5 cm²
Area of triangle PLQ
A2 = 1/2 × LQ × PL
Substituting the values
A2 = 1/2 × (4√5 - 6) × 8
A2 = 16√5 - 24 cm²
We know that
Area of triangle PLR = Area of triangle PLQ + Area of triangle PQR
Substituting the values
16√5 = 16√5 - 24 + Area of triangle PQR
Area of triangle PQR = 24 cm²
1/2 × PR × QM = 24
1/2 × 12 × QM = 24
QM = 4 cm
Therefore, QM is 4 cm.
✦ Try This: 144 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 16
In Fig. 9.21, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is a. 6 cm, b. 9 cm, c. 4 cm, d. 2 cm
Summary:
In Fig. 9.21, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is 4 cm
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