Question

In parallelogram EFGH, HK = 6x, KF = 2x + 8, GK = 3y, KE = y + 6. Find the perimeter of Angle KEF.​

Answer 1

Answer:

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Answer 2

$\color{red}\huge{\underline{\underline{GIVEN\dag}}}$

• Given quadrilateral is a Paralellogram.
• $KE=y+6$
• $KF=2x+8$
• $HG=6.8$
• $HK=6x$
• $GK=3y$

$\color{red}\huge{\underline{\underline{SOLUTION\dag}}}$

By the properties of paralellogram;

$HG=EF$

$\implies EF=6.8$

Perimeter of triangle KEF;

$EF+KE+KF=(6.8)+(y+6)+(2x+8)$

$\therefore{\boxed{Pr.(\triangle KEF)=2x+y+12.8}}......(1)$

But we know that;

In a Paralellogram diagonals are bisected.

$\implies HK=KF$

$\implies 6x=2x+8$

$\implies 4x=8$

${\boxed{\therefore x=2}}$

Similarly;

$GK=KE$

$\implies 3y=y+6$

$\implies 2y=6$

${\boxed{\therefore y=3}}$

Substituting 'x' & 'y' in (1);

$\implies Pr.(\triangle KEF)=2(2)+3+12.8$

$\therefore{\boxed{\color{orange}Pr.(\triangle KEF)=19.8}}$

HOPE THAT HELPS!!