Length of a rectangle is three times its breadth. Perimeter of the rectangle is 40 cm. Find its length and width.
Length = 15 cm, Breadth = 5 cm
Let the breadth be \(x\) cm.
Then the length is three times the breadth: \(3x\) cm.
Perimeter of a rectangle: \(P = 2( ext{length} + ext{breadth})\).
We are given \(P = 40\) cm. So,
\(40 = 2(3x + x)\)
Inside the bracket: \(3x + x = 4x\).
So, \(40 = 2(4x)\)
\(2(4x) = 8x\).
Therefore, \(40 = 8x\).
Divide both sides by 8: \(x = dfrac{40}{8} = 5\).
So, breadth \(= 5\) cm.
Length \(= 3 imes 5 = 15\) cm.
Check: \(2(15 + 5) = 2 imes 20 = 40\) cm ✓
Hence, Length = 15 cm, Breadth = 5 cm.