Question

Diagonal and area of the rectangle are 25 meters long and 168 metre .find the length of the rectangle

Answer 1

given that the length of the diagonal of a rectangle = 25 m , let L be the length and B be the breadth,

given, Area L × B = 168 m^2 ____eq.( 1 )

diagonal of rectangle( d)=√( L^2+B^2 )

√( L^2 + B^2 ) = 25

L^2 + B^2 = ( 25 )^2

L^2 + B^2 = 625

( L )^2 + ( B)^2 + 2×L×B -2×L×B = 625

( L - B )^2 + 2 L× B = 625

( L - B)^2 + 2 (168 ) = 625

( L - B )^2 + 336 = 625

( L - B)^2 = 625 - 336

( L - B )^2 = 289

L - B = 17

B = L - 17 __________eq. (2)

put value of " B" in eq. (1) , we get

L × ( L - 17 ) = 168

L^2 - 17 L - 168 = 0

L^2 - 24L + 7L - 168 = 0

L( L - 24 ) + 7 ( L - 24 ) = 0

( L - 24 ) ( L + 7 ) = 0

L =24 , -7

length can't be negative ,

therefore,length of rectangle (L)=24 m
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Your Answer: length=24m
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