Question

The length of a rectangular floor is 5m longer than its width. If the perimeter of the floor is 86m, find the dimensions of the floor.​

Answer 1

Answer:-

The length and breadth of the rectangular floor are 24m and 19 m.

Solution:-

Let:-

The length of rectangular floor be l . And its breadth be b .

According to the question, we have

Length of rectangular floor (l) = 5 + b

Given perimeter = 86 m

we know that ,

Perimeter of rectangle = 2 (l + b)

= > 86 = 2 ( l + b)

=> 86 = 2 ( 5+b + b)

=> 86 = 2 (5 + 2b)

=> 86/2 = 5 + 2b

=> 43 = 5 + 2b

=> 38 = 2b

=> 38/2 = b

=> 19 = b

Now:-

l = 5 + b = 5 + 19 = 24

Therefore:-

The length and breadth of the rectangular floor are 24m and 19 m.

Answer 2

Given :

• Length of the rectangular floor is 5 m longer than its width.
• Perimeter of the rectangular floor = 86 m

To Find :

• The dimensions of the rectangular floor.

Solution :-

Let the breadth of the rectangular floor be x m. Then, its length = (x+5) m

We know that,

$\bigstar{\boxed{\tt{Perimeter\: of\: rectangle=2 (length +breadth)}}}$

According to question ,

$: \implies{ \sf{Perimeter = 86}} \\ \\ : \implies{ \sf{2 [(x + 5) + x ] = 86}} \\ \\: \implies{ \sf{2 (x + 5 + x ) = 86}} \\ \\ : \implies{ \sf{2 (2x + 5)= 86}} \\ \\ : \implies{ \sf{4x + 10= 86 }} \\ \\ : \implies{ \sf{4x = 86 - 10}} \\ \\ : \implies{ \sf{4x = 76 }} \\ \\ : \implies{ \sf{x = \frac{76}{4} }} \\ \\ : \implies{ \boxed{ \tt{x = 19}}}$

$\underline{\bf{\therefore {The\:dimensions\:of\:the\:rectangular \:floor \:are\:19\:m \:and\:(19+5)\:m=24\:m.}}}$