Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 13

HARD

10th ICSE

IMPORTANT

Earn 100

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by $60$ . Assume the middle number to be $x$ and form a quadratic equation satisfying the above statement. Hence, find the three numbers.

Important Questions on Solving (Simple) Problems (Based On Quadratic Equations)

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 14

Out of three consecutive positive integers, the middle number is

p

. If three times the square of the largest is greater than the sum of the squares of the other two numbers by

67

; calculate the value of

p

.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 15

A can do a piece of work in

' x'

days and

B

can do the same work in

(x + 16)

days. If both working together can do it in

15

days; calculate

' x'

.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 16

One pipe can fill a cistern in

3

hours less than the other. The two pipes together can fill the cistern in

6

hours

40

minutes. Find the time that each pipe will take to fill the cistern.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 17

A positive number is divided into two parts such that the sum of the squares of the two parts is

20

. The square of the larger part is

8

times the smaller part. Taking

x

as the smaller part of the two parts, find the number.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 1

The sides of a right-angled triangle containing the right angle are

4 x cm

and

(2 x - 1) cm

. If the area of the triangle is

30 {cm}^{2}

; calculate the lengths of its sides.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 2

The hypotenuse of a right-angled triangle is

26 cm

and the sum of other two sides is

34 cm

. Find the lengths of its sides.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 3

The sides of a right-angled triangle are $(x - 1) cm, 3 x cm$ and $(3 x + 1) cm$ . Find:

the value of $x$ .

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 3

The sides of a right-angled triangle are $(x - 1) cm, 3 x cm$ and $(3 x + 1) cm$ . Find:

the lengths of its sides.