Question

The perimeter and area of a rectangular play ground are 80m2 and 384m2 respectively. Find the length and breadth of the play ground.

Answer 1

Given

• Perimeter of rectangle= 80m²
• Area of Rectangle= 384m²

To Find

• Length and Breadth

Formula used

$\boxed{\underline{Perimeter~of~Rectangle=2(Length+Breadth)}}$

$\boxed{\underline{Area \: of \: Rectangle=Length×Breadth}}$

Let

• Length be l
• Breadth be b

$\\\sf~~~ Perimeter~of~Rectangle= 2(Length+Breadth)$

${→\sf 2(Length+Breadth)=80}$

${→\sf\cancel{2}(Length+Breadth)=\cancel=80}$

${→\sf Length+Breadth=40}$

${→\sf Breadth=40-Length}$

$\boxed{\underline{Area \: of \: Rectangle=Length×Breadth}}$

Putting the Value of Breadth in Formula We get

$\\{→\sf384=Length×(40-Length)}$

${→\sf (Length)^{2} - 40Length+ 384 =0 }$

${→ \sf(Length)^{2} - 24Length - 16Length+ 384 =0 }$

${→\sf Length(Length - 24)- 16(Length+ 24) =0 }$

${→\sf ( Length - 16 ) (Length - 24)=0 }$

• Length of playground= 24 cm
• Breadth of playground =16 cm