in the square ABCD ,ac =(7x-2) cm and bd= (11x-10) cm ,ac is equal to.
Answers
Answer:
Seg AC is equal to 12 cm.
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
In figure, □ABCD is a square.
∴ AB = BC = CD = AD - - [ Sides of a square ]
AC = BD - - ( 1 ) [ Diagonals of a square are congruent ]
We have given that,
AC = ( 7x - 2 ) cm
BD = ( 11x - 10 ) cm
Now,
AC = BD - - [ From ( 1 ) ]
⇒ ( 7x - 2 ) = ( 11x - 10 )
⇒ 7x - 2 = 11x - 10
⇒ - 2 + 10 = 11x - 7x
⇒ 11x - 7x = - 2 + 10
⇒ 4x = 8
⇒ x = 8 ÷ 4
⇒ x = 2
Now,
AC = ( 7x - 2 )
⇒ AC = 7 * 2 - 2
⇒ AC = 14 - 2
⇒ AC = 12 cm
∴ Seg AC is equal to 12 cm.
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Verification:
AC = BD - - [ From ( 1 ) ]
We have, x = 2 and AC = 12.
∴ BD = 12
By substituting x = 2 in the RHS of BD = ( 11x - 10 ), we get,
RHS = ( 11x - 10 )
⇒ RHS = 11 * 2 - 10
⇒ RHS = 22 - 10
⇒ RHS = 12
LHS = BD = 12
∴ LHS = RHS
Hence verified!
Answer:
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Step-by-step explanation:
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