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.
