Question

1.If the area of the triangle is 36 cm2 and the height is 3 cm, the base of the triangle will be

2.A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 12 cm, find its breadth.​

Answer 1

Step by step explanation:-

Question- 1 :-

Given :-

• Area of triangle is 36cm²
• Height of triangle is 3 cm

To find :-

• Base of a triangle

Solution:-

As we know that ,

$area \: \: of \: \: triangle \: = \dfrac{1}{2} b \times h$

• b = base of triangle
• h = height of triangle

Let base of triangle be - b

Plugging values

$36 = \dfrac{1}{2} \times b \times 3$

$36 \times 2 = 3 \times b$

$12 \times 2 = b$

$b \: = 24cm$

So, base of a triangle is 24cm

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Question- 2:-

Given:-

• A wire is in shape of square of side 10cm
• After it bent into recatnge length 12 cm

To find :-

• Breadth of a rectangle

Solution:-

According to the problem,

Perimeter of square = Perimeter of rectangle beacuse first its shape is Square after bent down its shape is recatangle so, its Perimeter is equal

Perimeter of a square = 4a

Perimeter of rectangle = 2(l+b)

Perimeter of square = 4a

= 4(10) cm

= 40cm

Perimeter of a square = 40cm

Perimeter of rectangle = 2(12 + b)

ATQ ,

Perimeter of a square = Perimeter of rectangle

40 = 2(12+b)

40 = 24 + 2b

40 - 24 = 2b

16 = 2b

b = 8cm

So, Breadth of rectangle is 8cm

Answer 2

Question 1

Given :

• Area of the triangle = 36 cm²
• Height of the triangle = 3 cm

To find :

• Base of the triangle

Solution :

Formula of area of rectangle :-

• Area of rectangle = 1/2 × b × h

where,

• b denotes base of triangle
• h denotes height of triangle

Substituting the given values,

→ 36 = 1/2 × b × 3

→ 36 = 3/2 × b

→ 36 × 2/3 = b

→ 12 × 2 = b

→ 24 = b

Base of triangle = 24 cm

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VERIFICATION :

To verify the value of base of triangle, calculate the value of area of triangle, if it will be equal to 36 cm² (as mentioned in the question) then the value is right.

→ Area of triangle = 1/2 × b × h

Substituting the given values,

→ Area of triangle = 1/2 × 24 × 3

→ Area of triangle = 12 × 3

→ Area of triangle = 36

Area of triangle = 36 cm²

HENCE, VERIFIED.

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Question 2 :

Given :

• Side of square = 10 cm
• The wire is rebent into a rectangle of length 10 cm

To find :

• Breadth of the rectangle

Concept :

As we know,

• Whenever anything is changed from one shape into another. The perimeter always remains the same.

So, firstly we will calculate the perimeter of the wire which is square in shape by using the formula of perimeter of square. The resultant perimeter of square will be equal to Perimeter of rectangle. So, by using the formula of perimeter of rectangle, we will calculate the breadth of the rectangle.

Formula to calculate perimeter of square :-

• Perimeter of square = 4a

where,

• a denotes the side of the square

Formula to calculate perimeter of rectangle :-

• Perimeter of rectangle = 2(l + b)

where,

• l denotes length of the rectangle
• b denotes breadth of the rectangle

Solution :

Perimeter of square :-

→ Perimter of square = 4a

Substituting the given values,

→ Perimter = 4 × 10

→ Perimeter = 40 cm

Perimeter of the square = 40 cm

Perimeter of square = Perimeter rectangle

Perimeter of rectangle = 2(l + b)

→ 40 = 2(12 + b)

→ 40/2 = 12 + b

→ 20 = 12 + b

→ 20 - 12 = b

→ 8 = b

Therefore,

Breadth of the rectangle = 8 cm