Chapter 20. Perimeters and Areas of Plane figures NIOS Class 10 Mathematics Chapter-Wise Important Questions and Answers

Chapter 20: PERIMETERS AND AREAS OF PLANE FIGURES

Optional Questions and Answers for Algebraic Expressions and Polynomials [1 Mark]

CHECK YOUR PROGRESS 3.1

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Long Questions and Answers for Algebraic Expressions and Polynomials [ 3 or 4 Mark]

CHECK YOUR PROGRESS 20.1

1. Area of a square field is 225 m² . Find the perimeter of the field.

Solution: Let the side of the square be x (in m).

A/Q, x2=225

⇒x2=152⇒x=15 m

Therefore, the perimeter of the field =4x=4×15=60 m .

2. Find the diagonal of a square whose perimeter is 60 cm.

Solution: Let the side of the square be x m.

A/Q, 4x=60

⇒x=604⇒x=15 cm

Therefore, the diagonal of a square =2x²=x2=152 cm.

3. Length and breadth of a rectangular field are 22.5 m and 12.5 m respectively. Find:

(i) Area of the field

(ii) Length of the barbed wire required to fence the field .

Solution: Here, l=22.5 m and b=12.5 m

(i) Area of the rectangular field =l×b=22.5×12.5=281.25 m²

(ii) The length of the barbed wire required to fence the field =2l+b

=222.5+12.5=2×35=70 m

4. The length and breadth of rectangle are in the ratio 3 : 2. If the area of the rectangle is 726 m² , find its perimeter.

Solution: Let, 3x and 2x be the length and breadth of rectangle .

A/Q, 3x×2x=726

⇒6x2=726

⇒x2=7266=121

⇒x2=112

⇒x=11 m

Therefore, the perimeter of the rectangle =23x+2x

=2×5x=10×11=110 m

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