Question

The length of a rectangle is 3/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and length of this rectangle?

Answer 1

Question :

The length of a rectangle is 3/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and length of this rectangle?

Solution :

$\underline{\bold{Given:}}$

• The perimeter of the rectangle = $15\frac{1}{3}\:cm=\frac{46}{3}\:cm$
• The length of the rectangle is longer than the width by $\frac{3}{6}\:cm$

$\underline{\bold{To\:Find:}}$

• The width of the rectangle.
• The length of the rectangle.

$\rule{193}{1}$

Let the width of the rectangle be x cm.

Then, its length = $(x+\frac{3}{6}) \:cm$

$\boxed{\purple{Perimeter =2(L+W)}}$

$\implies Perimeter =2(L+W) \\\implies \frac{46}{3} =2( x + \frac{3}{6} + x) \\ \implies \frac{46}{3} = 2( 2x + \frac{3}{6} ) \\ \implies \frac{46}{3} = 4x + 1 \\ \implies \frac{46}{3} - 1 = 4x \\ \implies \frac{46 - 3}{3} = 4x \\ \implies \frac{43}{3} = 4x \\ \implies \frac{43}{3}\times \frac{1}{4} =x \\ \implies \frac{43}{12} = x \\ \implies x = 3\frac{7}{12}$

$\boxed{\green{\therefore{The\: width\: of\: the\: rectangle =3\frac{7}{12}\:cm.}}}$

$\implies The\: length\: of\: the\: rectangle = (\frac{43}{12} + \frac{3}{6})\:cm\\\implies The\: length\: of\: the\: rectangle =(\frac {43+6}{12})\:cm\\\implies The\: length\: of\: the\: rectangle=\frac {49}{12}\:cm\\\implies The\: length\: of\: the\: rectangle=4\frac{1}{12}\:cm$

$\boxed{\green{\therefore{The\: length\: of\: the\: rectangle=4\frac{1}{12}\:cm.}}}$

Answer 2

$\bold\pink{SOLUTION:}$

The width and length of

this rectangle are 3 7/12 cm and 4

1/12 cm cm respectively.

Let the breadth of the rectangle be 'b'cm

Given, the length of the rectangle is 3/6 cm (=0.5 cm) longer than breadth.

So, length = (b + 0.5) cm

We know, perimeter of a rectangle is equal to 2(l+b), where l and b are the length and breadth of the rectangle.

So, perimeter = 2(b+0.5+b) = 2(2b + 0.5)cm.

Given, perimeter equals to 15 \frac{1}{3} cm, which is 46/3 cm.

So, 2(2b + 0.5) = 46/3

⇒(2b + 0.5) = 23/3

⇒ 2b = 23/3 - 0.5 = 21.5/3

⇒ b = 21.5/6 = 43/12

$= 3\frac{7}{12} cm$

This is the breadth.

Length = (b + 0.5)cm

$= (43/12 + 0.5)cm = 49/12 cm \\ </p><p></p><p>= 4 \frac{1}{12} cm$ (ANSWER)

$<marquee>$ HOPE ITS HELP U