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Solve for the missing numbers:

1. Length is 3 times the breadth.

2. Given:
- Perimeter of the rectangle = 40 cm

3. Perimeter formula:
- [tex]\( 2(\text{length} + \text{breadth}) = 40 \)[/tex]

4. Calculations:
- [tex]\( 2(\square x + \square x) = 40 \)[/tex]
- [tex]\( 2 \times \square x = 40 \)[/tex]
- [tex]\( \square x = 20 \)[/tex]
- [tex]\( x = 5 \)[/tex]

Therefore:
- Breadth of rectangle = [tex]\(\square\)[/tex] cm
- Length of rectangle = [tex]\(\quad \quad \)[/tex] cm



Answer :

GinnyAnswer
Certainly! Let's provide the step-by-step solution with all the correct numbers filled in:

Given:
- Length is 3 times the breadth
- The perimeter of the rectangle is [tex]\(40\)[/tex] cm

Let's denote:
- [tex]\(x\)[/tex] as the breadth of the rectangle in cm
- [tex]\(3x\)[/tex] as the length of the rectangle in cm

The perimeter [tex]\(P\)[/tex] of a rectangle is given by the formula:
[tex]\[ P = 2(\text{length} + \text{breadth}) \][/tex]

Substitute the given perimeter and the expressions for the length and breadth into the formula:
[tex]\[ 2(3x + x) = 40 \][/tex]

Simplify inside the parentheses:
[tex]\[ 2(4x) = 40 \][/tex]

Perform the multiplication:
[tex]\[ 8x = 40 \][/tex]

Solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{40}{8} \][/tex]
[tex]\[ x = 5 \][/tex]

So, the breadth of the rectangle is [tex]\(5\)[/tex] cm.

Since the length is 3 times the breadth:
[tex]\[ \text{Length} = 3 \times 5 = 15 \, \text{cm} \][/tex]

Now, putting it all together:

To complete the boxes:
[tex]\[ \begin{array}{r} 2(\underline{3}x+\underline{1}x)=40 \\ 2 \times \underline{4}x=40 \\ \underline{8}x=40 \\ x=5 \end{array} \][/tex]

Therefore, the breadth of the rectangle is [tex]\( \underline{5} \)[/tex] cm, and the length of the rectangle is [tex]\( \underline{15} \)[/tex] cm.

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