Page 177 - Start Up Mathematics_7

In ∆ ACD,
2
2
AD = AC + CD 2 (Pythagoras property)
2
2
2
⇒ AD = 5 + 12 = 169
⇒ AD = 13 cm
Example 23: A box is 8 cm long and 6 cm wide. If the height of the box is 24 cm, find the length
of the longest stick l which can come completely inside the box.
Solution: In ∆ DCB, H G
2
2
2
2
2
BD = DC + CB = 8 + 6 (Pythagoras property) E F
2
⇒ BD = 100
⇒ BD = 10 cm l 24 cm
In ∆ HDB,
2
2
2
2
HB = HD + DB = 24 + 10 2 (Pythagoras property)
2
⇒ l = 576 + 100 = 676 D C
⇒ l = 26 cm 6 cm
A 8 cm B
EXERCISE 10.2
1. Is it possible to have a triangle with the following sides?
(a) 6 cm, 8 cm and 9 cm (b) 5 cm, 12 cm and 18 cm
(c) 1 cm, 1 cm and 1 cm (d) 3 cm, 4 cm and 5 cm P

2. In ∆ PQR, PS is the median of the triangle. Which one of
the following is always true?
(a) PQ + QR + RP > 3 PS
(b) PQ + QR + RP > 2 PS

(c) PQ + QR + RP > PS Q S R
3. We know in a triangle sum of any two sides is greater than the third side. Is the sum of
any two angles of a triangle also greater than the third angle? Justify or contradict with an
example.
4. Take any point O in the interior of ∆ ABC as shown. State which A
of the following is true?
(a) AO + BO > AB (b) BO + CO > BC O

(c) CO + AO > CA (d) AB + AC < BC
(e) AB + BC + CA < 2(AO + BO + CO) B C
5. The lengths of two sides of a triangle are 10 cm and 15 cm. Between what two measures
should the length of the third side lie?

6. The lengths of two sides of a triangle are 8 cm and 10 cm. Between what two measures
should the length of the third side lie?
7. Which of the following can be the sides of a right-angled triangle?
(a) 0.5 cm, 1.2 cm and 1.3 cm (b) 2.4 cm, 3.2 cm and 7.9 cm

(c) 5.0 cm, 5.25 cm and 7.25 cm (d) 1.6 cm, 3.0 cm and 3.4 cm

169