Question

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

Answer 1

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Answer 2

Given :

• The length of a rectangular floor is 5 m longer than its width.

• Perimeter of the floor = 86 m.

To Find :

• The dimensions of the floor = ?

Formulas to be used :

• Perimeter of rectangle = 2(l + b).

Solution :

Let the length of the rectangle be l and breadth be b.

According to the condition,

Length of rectangular floor (l) = 5 + b.

Given perimeter = 86 cm.

Now,

We know that,

$\purple {\underline {\boxed {\bf Perimeter \ of \ rectangle \ = \ 2 (l \ + \ b)}}}$

$\qquad : \implies \sf 86 \ = \ 2(l \ + \ b)$

$\qquad : \implies \sf 86 \ = \ 2(5 \ + \ b + \ b)$

$\qquad : \implies \sf 86 \ = \ 2(5 \ + \ 2b)$

$\qquad : \implies \sf \dfrac {86}{5} \ = \ 5 \ + \ 2b$

$\qquad : \implies \sf 43 \ = \ 5 \ + \ 2b$

$\qquad : \implies \sf 43 \ - \ 5 \ = \ 2b$

$\qquad : \implies \sf 38 \ = \ 2b$

$\qquad : \implies \sf \dfrac {38}{2} \ = \ 2b$

$\qquad : \implies \sf B \ = \ 19 \ m$

$\qquad \blue {\underline {\boxed {\sf Breadth \ = \ 19 \ m}}}$

Now,

$\qquad : \implies \sf l \ = \ 5 \ + \ b$

$\qquad : \implies \sf l \ = \ 5 \ + \ 19$

$\qquad : \implies \sf l \ = \ 24 \ m$

$\qquad \blue {\underline {\boxed {\sf Length \ = \ 24 \ m}}}$

$\therefore$ The length and breath is 24 m and 19 m respectively.