2 Marks Questions

Question 12 Marks

Can you draw any inferences from this exercise? Please write it here.

Answer

Congruence: The triangles are congruent, meaning all corresponding sides and angles are equal.
Area: Since the triangles are congruent, their areas are identical.

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Question 22 Marks

Make a figure with a perimeter of 18 units.

Answer

One possible figure is an L-shaped arrangement:
Arrange 6 squares in a vertical line and 3 squares in a horizontal line at the bottom.

Perimeter = 6 + 3 + 1 + 1 + 1 + 1 + 1 + 1 + 3 = 18 units.

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Question 32 Marks

What is the largest perimeter possible?

Answer

The largest perimeter is achieved by arranging the squares in a straight line:

Perimeter = 1 + 9 + 1 + 9 = 20 units.

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Question 42 Marks

What is the smallest perimeter possible?

Answer

The smallest perimeter is achieved by forming a 3 × 3 square:

Perimeter = 3 + 3 + 3 + 3 = 12 units.

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Question 52 Marks

The area of a rectangular garden that is 50 m long is 1000 sq m. Find the width of the garden.

Answer

Width of rectangular garden $=\frac{\text { area }}{\text { length of garden }}$
$\begin{array}{l}=\frac{1000}{50} \\ =20 m .\end{array}$

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Question 62 Marks

Are the perimeters of the square and the rectangle formed from these 7 pieces different or the same? Give an explanation for your answer.

Answer

For the same area, a square always has the smallest perimeter.
So the perimeter of the square is less than that of the rectangle.

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Question 72 Marks

Which shape has more area: Shape F or G? Give reasons for your answer.

Answer

Since the medium triangle and the rhomboid are each made up of two small tangram triangles, they each have an area 2x that of the small triangle. Hence both have the same area.

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Question 82 Marks

Explore and figure out how many pieces have the same area.

Answer

Here, we can see that some shapes have identical areas.
Specifically
Shapes A and B These shapes are identical, meaning they cover the same amount of space, so they have the ^ same area.
Shapes C and E These shapes also have the same area because they are identical in size and shape.

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Question 92 Marks

A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m, what is the maximum number of trees that can be planted in this grove?

Answer

Area of rectangular coconut grove = 100 × 50 = 5000 sq. m
Given each coconut tree requires 25 sq. m
then the maximum no. of trees that can be planted in this grove = $\frac{5000}{25}=200$

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Question 102 Marks

The area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden?

Answer

Length of a rectangular garden $=25 m$
Area of rectangular garden $=$ length × width $300 sq m =25 m \times$ width
⇒ Width of the garden $=\frac{300 sqm }{25 m}=12 m$

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Question 112 Marks

What would be the cost of fencing a rectangular park whose length is 150 m and breadth is 120 m if the fence costs ₹ 40 per meter?

Answer

The length of the fence is the perimeter of the rectangular park.
Given that the length of the rectangular park = 150 m and breadth = 120 m
∴ Perimeter = 2(l + b)
= 2(150 + 120)
= 2(270)
= 540 m
Now cost of fencing per meter = ₹ 40
Cost of fencing the rectangular park = ₹ 40 × 540 = ₹ 21600

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Question 122 Marks

Find the length of the third side of a triangle with a perimeter of 55 cm and two sides of length 20 cm and 14 cm, respectively.

Answer

Let ABC be the given triangle such that AB = 20 cm, BC = 14 cm
So, perimeter = AB + BC + CA = 55 cm
⇒ 55 = 20 + 14 + CA
⇒ CA = 55 – (20 + 14)
⇒ CA = 21 cm
∴ the length of the third side of the triangle = 21 cm.

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Question 132 Marks

Find the missing terms :
Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?

Answer

Perimeter of a rectangle = 12 m
⇒ 2 (length + breadth) = 12 m
⇒ 3 m + breadth = 6 m
⇒ breadth = 3 m

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Question 142 Marks

Find the missing terms :
Perimeter of a square = 20 cm; length of a side = ?

Answer

Given, perimeter of a square = 20 cm
⇒ 4 × side = 20 cm
⇒ side = 5 cm
Therefore, length of a side = 5 cm

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Question 152 Marks

Find the missing terms :
Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?.

Answer

Given, perimeter of rectangle =14 cm, breadth = 2 cm
Perimeter of rectangle = 2 (length + breadth)
⇒ 14 cm = 2 (length + 2 cm)
⇒ 7 cm = length + 2 cm
⇒ length = 5 cm

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