Maths

148 MATHEMATICS
Solution : Let AB be the ladder and CA be the wall
with the window at A (see Fig. 6.49).
Also,
From Pythagoras Theorem, we have:
BC = 2.5 m and CA = 6 m
AB 2 =BC 2 + CA 2
= (2.5) 2 + (6) 2
= 42.25
So, AB = 6.5
Thus, length of the ladder is 6.5 m.
Example 12 : In Fig. 6.50, if AD BC, prove that Fig. 6.49
AB 2 + CD 2 = BD 2 + AC 2 .
Solution : From ✁ ADC, we have
AC 2 =AD 2 + CD 2
(Pythagoras Theorem) (1)
From ADB, we have
✁
AB 2 =AD 2 + BD 2
(Pythagoras Theorem) (2)
Subtracting (1) from (2), we have
Fig. 6.50
AB 2 – AC 2 =BD 2 – CD 2
or, AB 2 + CD 2 =BD 2 + AC 2
Example 13 : BL and CM are medians of a
triangle ABC right angled at A. Prove that
4 (BL 2 + CM 2 ) = 5 BC 2 .
Solution : BL and CM are medians of the
ABC in which A ✁ = 90° (see ✂ Fig. 6.51).
From ABC,
Fig. 6.51
✁
BC 2 =AB 2 + AC 2 (Pythagoras Theorem) (1)
✁ From ABL,
BL 2 =AL 2 + AB 2