Page 15 - CHAPTER 4 (Quadratic equations)

CHAPTER 4
QUADRATIC EQUATIONS

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⇒(y-9)(2y-11)= 0 ⇒y=9 or y=
2

11
11
∵y= is not possible [∵ <7]
2 2
So, y = 9.

∴ 5 ×9+9 =27 [from (ii)]
2
Hence, Varun's present age is 27 years, and Swati's present age is 9

years.

Example 4: The length of hypotenuse of a right triangle exceeds the

length of the base by 2cm and exceeds twice the length of the altitude

by 1cm. Find the lengths of all sides of the triangle.

Solution:

Let AB = x. Then

AC = (2x +1) and BC = (2x +1) –2 = 2x – 1

⇒ ∆ABC, AC² = AB² + BC² [By Pythagoras

theorem]

⇒ (2x + 1)² = x² + (2x –1)² ⇒ 4x² + 4x + 1 = x² + 4x² – 4x + 1

⇒ x² = 8x ⇒ 8 cm

∴ BC = 2x – 1 = 2 × 8 – 1 = 15cm

AC = 2x + 1 = 2 × 8 + 1 = 17cm

So, the sides of the given triangle are 8cm, 15cm and 17cm.

Example 5: A train travels 360km at a uniform speed. If the speed had

been 5km/h more, it would have taken 1 hour less for the same journey.

Find the speed of the train.

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