Question

The length of a rectangular hallway in 3 times it's breadth. if the perimeter of the hallways is 48 m find its length and breadth​

Answer 1

Answer:

length = 3x

Breadth = x

Perimeter= 2( l+b ) =48m

=2 ( 3x+x) = 2(4x) = 8x

= x = 6m

Hence, the breadth is 6m and length is 18m.

Answer 2

Answer:

$\red\bigstar$ Breadth of the rectangular Hallway = 6 m.

$\red\bigstar$ Length of the rectangular Hallway = 18 m.

The Hallway's Diagram

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 18 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 6 m}\put(-0.5,-0.4){\bf }\put(-0.5,3.2){\bf }\put(5.3,-0.4){\bf }\put(5.3,3.2){\bf }\end{picture}$

SOLUTION

Let us Assume that the Breadth(b) of the rectangular hallway = 'x'.

From the question , the length of the rectangular hallway in 3 times it's breadth.

$\implies$

Length(l) of the hallway = 3x.$\longrightarrow$(1)

Perimeter of a rectangle = 2(l+b)

Here,

Perimeter = 48m.

Length(l) = 3x.

Breadth(b) = x.

$\implies$

48 = 2(x+3x)

$\implies$

48 = 2x + 6x

$\implies$

48 = 8x

$\implies$

$\sf x = \dfrac{48}{8}$

✳ The value of Breadth , x = 6m.

Let us substitute the value of x = 6m. in (1) then,

✳ Length of the hallway = 3 × 6 = 18m.