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Sagot :
Answer:
10/9 cm
Step-by-step explanation:
To find the breadth of the rectangle, we use the information given about its dimensions:
Let the length of the rectangle be \( 5x + 15 \) cm.
Let the breadth of the rectangle be \( 4x - 6 \) cm.
We are given that the perimeter of the rectangle is 50 cm.
The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2 \times (\text{length} + \text{breadth}) \]
Substituting the given values:
\[ 50 = 2 \times ((5x + 15) + (4x - 6)) \]
Now, simplify the expression inside the parentheses:
\[ 50 = 2 \times (5x + 15 + 4x - 6) \]
\[ 50 = 2 \times (9x + 9) \]
Next, divide both sides by 2 to solve for \( 9x + 9 \):
\[ 25 = 9x + 9 \]
Subtract 9 from both sides:
\[ 25 - 9 = 9x \]
\[ 16 = 9x \]
Now, divide both sides by 9 to solve for \( x \):
\[ x = \frac{16}{9} \]
Now that we have \( x \), substitute it back into the expression for the breadth \( 4x - 6 \):
\[ \text{Breadth} = 4x - 6 \]
\[ \text{Breadth} = 4 \left(\frac{16}{9}\right) - 6 \]
\[ \text{Breadth} = \frac{64}{9} - \frac{54}{9} \]
\[ \text{Breadth} = \frac{10}{9} \]
Therefore, the breadth of the rectangle is 10/9 cm.
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