Question

The perimeter of the top of a rectangular table is 28 m, whereas its area is 48 m2. what is the length of its diagonal?

Answer 1

Perimeter of Rectangle = 28 m

2( length + breadth ) = 28

length + breadth = 14 ----- : ( 1 )





Area of Rectangle = 48 m^2

Length × Breadth = 48 ------- : ( 2 )






In ( 1 ), square on both sides,


( length + breadth )^2 = ( 14 )^2
.

length^2 + breadth^2 + 2( length × breadth ) = 784


$\bold{ \underline{ \: putting \: the \: value \: of \: (length \: \times breadth \: ) \: from \: ( \: 1 \: )}}$


length^2 + breadth^2 + 2( 48 ) = 196


length^2 + breadth^2 = 196 - 96


length^2 + breadth^2 = 100 m^2


√( length^2 + breadth^2 ) = 10 m----- : ( 3 )





We Know, Diagonal of Rectangle = √ { length^2 +breadth^2 }

$\bold{ \underline{ \: putting \: the \: value \: from \: ( \: 3 \: )}}$


Hence, Length of its diagonal = 10 m

Answer 2

Perimeter of Rectangle = 28 m
2( length +Breadth ) = 28 m
length + breadth = 14 m ----:( 1 ) equation



Area of Rectangle = 48 m^2
Length × breadth = 48m^2 ----:( 2 ) equation




On 1 equation,

length + Breadth = 14



Square on both sides,

Length^2 + Breadth^2 +2( 48 ) = 196 m^2


Have put the value of length × breadth


Length^2 + breadth^2 = 196 - 96

Length^2 + breadth^2 = 100




We know, diagonal of Rectangle = √length^2 + breadth^2


So, diagonal = √100 m^2

Length of diagonal = 10m
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