Question

The sides of a rectangular park are in the ratio 4 : 3 if it's area is 2028 sq. m, find the cost of fencing​

Answer 1

Correct Question:-

The sides of a rectangular park are in the ratio 4 : 3 if it's area is 2028 m², find the sides of the rectangular park.

Given:-

• Area of rectangle = 2028 m²
• Ratio of sides of rectangle = 4 : 3

To Find:-

• Sides of rectangle

Solution:-

Put x in the ratio,

• Length of rectangle = 4x
• Breadth of rectangle = 3x

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ \mathfrak{ \underline{ \green{Formula \: to \: calculate \: the \: area \: of \: rectangle}}}$

$\underline {\boxed{ \mathfrak{ \star \: \: \: \: { \red{ \large{area = length \times breadth}}}}}}$

According to question,

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \: \: \:4x \times 3x = 2028}$

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \: \: \:12 {x}^{2} = 2028}$

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \: \: \: {x}^{2} = \frac{2028}{12}}$

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \: \: \: {x}^{2} = 169}$

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \: \: \:x = \sqrt{169} }$

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \mathfrak{ \purple{x = 13}}}}}$

Now,

• Length of rectangle = 4x = 52 cm
• Breadth of rectangle = 3x = 39 cm

Hence:-

• The sides of rectangular park are 52 cm and 39 cm.