Question

12. Find the perimeter of a rectangular park whose length and breadth are
45 1/2 m and 34 3/4m.​

Answer 1

• The perimeter of the rectangle = $\sf{160\dfrac{1}{2}}$ m.

Given :

• The length of a rectangle = $\sf 45\dfrac{1}{2}$ m.
• The breadth of a rectangle = $\sf 34\dfrac{3}{4}$ m.

To Find :

• The perimeter of the rectangle.

Solution :

We have to find the perimeter of the rectangle. We can use formula,

$\star \: \: \: \: \boxed{\bf{\orange{Perimeter = 2(l + b)}}}$

The given values of the length of the rectangle and the breadth of the rectangle are in the form of mixed fraction.

First, we need to change the mixed fraction to simple fraction.

For changing the mixed fraction to simple fraction, multiply the whole number (front number of the fraction) by the denominator then add the result from the numerator and the numerator remains same.

So,

• Length (l) = $\sf 45\dfrac{1}{2}$ m.

$\bf\implies\dfrac{(45 \times 2) + 1}{2} \: m\\ \\ \\ \bf\implies \dfrac{90 + 1}{2} \: m\\ \\ \\ \bf\implies \dfrac{91}{2} \: m$

Therefore,

• Length (l) = $\sf\dfrac{91}{2}$ m.

Now,

• Breadth (b) = $\sf 34\dfrac{3}{4}$ m.

$\bf\implies \dfrac{(34 \times 4) + 3}{4} \: m\\ \\ \\ \bf\implies \dfrac{136 + 3}{4} \: m\\ \\ \\ \bf\implies \dfrac{139}{4} \: m$

Therefore,

• Breadth (b) = $\sf\dfrac{139}{4}$ m.

Now, substitute both the given values in the formula of the perimeter of a rectangle.

$\bf\implies2\:\bigg( \dfrac{91}{2} + \dfrac{139}{4}\bigg) \: m\\ \\ \\\bf\implies 2 \: \bigg( \dfrac{(91 \times 2) + (139 \times1)}{4}\bigg) \: m\\ \\ \\\bf\implies2\: \bigg(\dfrac{182+139}{4}\bigg) \: m\\ \\ \\ \bf\implies \not2 \times \dfrac{321}{ \not4} \: m\\ \\ \\ \bf\implies \dfrac{321}{2} \: m$

Now, change this simple fraction to mixed fracrion.

For changing the simple fraction to mixed fraction, we need to divide the fraction. After dividing, we obtain a remainder as a numerator, a quotient as a whole number (front number of the fraction) and a divisor as a denominator.

$\bf\Large\qquad\quad160\\ \begin{array}{cc} \cline{2 - 2}\sf 2)&\sf \ \ 3 \ 2 \ 1\\&\sf-2 \ \ \ \ \ \\ \cline{2-2}& \sf\ 1 \ 2\ \ \\&\sf\ -1 \ 2 \ \ \ \ \\ \cline{2-2} & \sf \ 0 \ 0 \ \ 1 \\ \cline{2-2} \end{array}$

• Reamainder = 1.
• Quotient = 160.
• Divisor = 2.

Therefore,

The mixed fraction will be :-

$\bf\implies (quotient) \: \dfrac{(remainder)}{(divisor)} \\ \\ \\ \bf\implies160 \: \dfrac{1}{2} \: m$

Hence,

The perimeter of the rectangle is $\sf{160\dfrac{1}{2}}$ m.

Answer 2

Answer:

Given :

• Length = 45 1 /2 m= 91/2 m

• Breadth = 34 3/4 m= 139/4 m

To Find :

• Find the perimeter of a rectangular park

Solution :

Perimeter of Rectangle = 2 × (L + B)

Concept :

if only the the area is stated :

• it's sure and obvious that they'll mention one of the sides. and when when one side's length and the area is mentioned then it becomes to formulate.

Now, as we have both length and breadth we can formulate the perimeter. 

P = 2(l + b)

Substitute All values :

Perimeter of Rectangle = 2 × (91/2 + 139/4)

Perimeter of Rectangle = 2 × 321/4

Perimeter of Rectangle = 321/2

Perimeter of Rectangle = 160 1/2 m.

Hence , the perimeter of a rectangular 160 1/2 m