Page 175 - Start Up Mathematics_7

Example 16: Find the unknown length x in the following figures.

24
10 10
x x 10 6
3 x 7
x
4 8
(a) (b) (c) (d)
Solution: Applying Pythagoras property, we get Do you know?

2
2
(a) x = 3 + 4 2 Pythagoras was a Greek philosopher and
2
⇒ x = 9 + 16 = 25 = 5 2 mathematician who was born in 570 BC.
He formed a society named as Pythagorean
⇒ x = 5 units society.
2
2
(b) x + 8 = 10 2 He discovered Pythagoras theorem which
2
2
⇒ x = 10 – 8 2 states that in a right
2
⇒ x = 36 triangle the square
of the hypo tenuse is
⇒ x = 6 units equal to the sum of
the squares of the
2
2
2
(c) x = 24 + 7 = 625 = 25 2 other two sides by
⇒ x = 25 looking at the floor
tiles.
2
(d) + 6 = 10 2 Besides Pythagoras theorem, the discovery
of irrational numbers is also attributed to the
members of the Pythagorean society. This
⇒ = 100 – 36 = 64 = 8 2 discovery was one of the greatest events in
the history of Mathematics.
⇒ = 8

⇒ x = 16 units

Example 17: Which of the following can be the sides of a right-angled triangle?

(a) 1.5 cm, 2.5 cm, 2 cm (b) 3 cm, 3 cm, 5 cm
In case of right-angled triangles, identify the right angle.

Solution: In each case we verify whether or not
2
2
(Hypotenuse) = (Base) + (Perpendicular) 2
2
or (Longest side) = Sum of squares of the other two sides
2
2
(a) 1.5 + 2 = 2.25 + 4 = 6.25
2
Also, 2.5 = 6.25
2
2
Thus, 1.5 + 2 = 2.25 2
Hence, these sides form a right-angled triangle and the angle opposite the side
measuring 2.5 cm is a right angle.
2
2
2
(b) 3 + 3 = 9 + 9 = 18 ≠ 5 . Hence, these sides do not form a right-angled triangle.
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