Question

Length of a rectangle is 8 m less than twice its breadth. If the perimeter of the
rectangle is 56 m, find its length and breadth.​

Answer 1

❍ Let the length of rectangle be (2x - 8) m and breadth of rectangle be x respectively.

________________________

$\underline{\bigstar\boldsymbol{According\;to\;the\;given\;Question:}}$

• Length of a rectangle is 8 m less than twice its breadth. Let the value be (2x - 8)
• Perimeter of rectangle is 56 m.

$\Large{\underline{\frak{\pink{\dag\;As\;we\;know\;that:}}}}$

$\red{\bigstar}\;\underline{\boxed{\sf{Perimeter\;of\;rectangle\;=\;2(l+b)}}}$

Therefore,

Let us apply the given values,

$\\ \longrightarrow\sf{56 = 2\bigg((2x-8)+x\bigg)}\\ \\ \\ \longrightarrow\sf{56 =2(3x-8)}\\ \\ \\ \longrightarrow\sf{56=6x-16}\\ \\ \\ \longrightarrow\sf{56 + 16 = 6x}\\ \\ \\\longrightarrow\sf{72=6x} \\ \\ \\\longrightarrow\sf{x =\cancel{\frac{72}{6}}} \\ \\ \\ \longrightarrow\boxed{\frak{x=12}}\;\blue{\bigstar}$

Hence,

• Length of rectangle = (2×12 - 8) = (24-8) = 16 m.
• Breadth of rectangle = 12 m.