Question

The perimeter of a rectangle is 44 cm. If one of the two adjacent sides is 1.8 cm longer than the other, what are the lengths of the sides?​

Answer 1

☆ Given :

• Perimeter of rectangle = 44 cm

• One of the adjacent side is 1.8 cm longer than other.

☆ To find :

• The Length

• The Breadth

☆ Solution :

Let the breadth of the rectangle be x

Than length of the rectangle will be x + 1.8

Perimeter of rectangle = 2(length + breadth)

⟼ 44 = 2(x + 1.8 + x)

⟼ 44 = 2(x + x + 1.8)

⟼ 44 = 2(2x + 1.8)

⟼ 44 = 4x + 3.6

⟼ 44 - 3.6 = 4x

⟼ 40.4 = 4x

⟼ 40.4/4 = x

⟼ 10.1 = x

∴ The Breadth (x) = 10.1 cm

And, length (x + 1.8) = 10.1 + 1.8 = 11.9 cm

★ Check :—

Perimeter of rectangle = 2(l + b)

→ 44 = 2(11.9 + 10.1)

→ 44 = 2(22)

→ 44 = 2 × 22

→ 44 = 44

Thus, both sides are equal.

Hence checked !

Answer 2

$\mathcal{\underline{ \underline{Given:- }}}$

$• \sf \: The \: perimeter \: of \: a \: rectangle \: is \: 44 \: cm.$

$• \sf \: One \: of \: the \: two \: adjacent \: sides \: is \: 1.8 \: cm \: longer \: than \: the \: other.$

$\mathcal{\underline{ \underline{To \: Find :- }}}$

$• \sf \: The \: lengths \: of \: the \: sides.$

$\mathcal{\underline{ \underline{Solution :- }}}$

$\sf{We \: know \: that, }$

$\bf \red{ \star \: {Perimeter \: of \: a \: rectangle \: = \: 2 (length + breadth) \: unit}}$

$\sf{According \: to \: the \: question, }$

$\sf\: {Let \: the \: length \: be \: x \: cm }$

$\therefore \sf breadth \: will \: be \: (x + 1.8) \: cm$

$\therefore \sf44 = 2(x + x + 1.8)$

$\rightarrow \sf44 = 2(2x + 1.8)$

$\rightarrow \sf22 = 2x + 1.8$

$\rightarrow \sf2x + 1.8 = 22$

$\rightarrow \sf2x = 20.2$

$\rightarrow \sf x= 10.1$

$\sf \pink{Therefore, \: length \: is \: 10.1 \: cm \: and}$

$\sf \pink{breadth \: is \: (10.1 + 1.8) \: cm = 11.9 \: cm}$

$\bf \underline{Correction \: Test}$

$\sf{Perimeter \: of \: the \: rectangle =2(10.1 + 11.9) \: cm }$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =( 2 \times 22) \: cm$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =44 \: cm$

$\bf{Hence, Answers \: are \: 10.1 \: cm \: and \: 11.9 \: cm. }$