# Question 2:

The sum of areas of two squares is 157 m². If the sum of their perimeters is 68 m, find the sides of the two squares.                     [CBSE 2019]

## Solution:

Let the side of first square = x m

And side of second square = y m

According to the question

4 x + 4y = 68 m

⇒ 4 y = 68 – 4 x

⇒  4 y = 4(17 – x)

⇒  y   =  17 – x

Again from the question

x² + y² = 157

⇒ x² + (17 – x)² = 157

⇒   x² + 289 + x² – 34 x = 157

⇒  2 x² – 34 x + 289 -157 = 0

⇒  2 x² – 34 x + 132 = 0

⇒   x² – 17 x + 66 = 0

⇒   x² – 11 x – 6 x + 66 = 0

⇒   x(x – 11) – 6(x – 11) = 0

⇒ (x – 11)(x – 6) = 0

⇒ x = 11, 6

Hence, side of small square = 6 m

And the side of large square = 11 m

# Question:1

If Ritu were younger by 5 years than what she really is, then the square of her age would have been 11 more than five times her present age. What is her present age ?                   [CBSE Term-2 SQP 2022]

# Question 3:

If the equation (1 + m²)x² + 2 mcx + c² – a² = 0 has equal roots then show that c² = a²(1 + m²).

[CBSE 2017]

# Question 4:

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, it would have taken 3 hours more to cover the same distance. Find the original speed of the train.                [CBSE    2020]

# Question 5:

In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200km/hr and time of flight increased by 30 minutes. Find the original duration of flight .      [CBSE  2020]

# Question 6:

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hours less for the same journey. Find the speed of the train.                                                                                   [CBSE  2019] 