If A B C D E F is a regular hexagon with A B = a and B C = b, then C E equals

Question

If A B C D E F is a regular hexagon with A B = a and B C = b, then C E equals (A) b - a (B) -b (C) b - 2a (D) None of these

Tardigrade Admin · Accepted Answer

In triangle A B C, A B+B C=A C <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/c11178ebf69eca6a4492e173bb1d4b31-.png" /> ⇒ A C = a + b A D is parallel to B C and A D=2 B C ∴ A D =2 b In triangle A C D, A C+C D=A D ⇒ C D=2 b-(a+ b)=b-a Now, C E = C D + D E = b -2 a

Q. If $A BC D EF$ is a regular hexagon with $A B = a$ and $BC = b$ , then $CE$ equals

b - a

-b

b - 2a

None of these

In $△ A BC, A B + BC = A C$

$\Rightarrow A C = a + b$
$A D$ is parallel to $BC$ and $A D = 2 BC$
$∴ A D = 2 b$
In $△ A C D, A C + C D = A D$
$\Rightarrow C D = 2 b - (a + b) = b - a$
Now, $CE = C D + D E = b - 2 a$

Q. If ABCDEF is a regular hexagon with AB=a and BC=b, then CE equals

b - a

-b

b - 2a

None of these

In △ABC,AB+BC=AC ⇒AC=a+b AD is parallel to BC and AD=2BC ∴AD=2b In △ACD,AC+CD=AD ⇒CD=2b−(a+b)=b−a Now, CE=CD+DE=b−2a

Q. If $A BC D EF$ is a regular hexagon with $A B = a$ and $BC = b$ , then $CE$ equals

In $△ A BC, A B + BC = A C$

$\Rightarrow A C = a + b$
$A D$ is parallel to $BC$ and $A D = 2 BC$
$∴ A D = 2 b$
In $△ A C D, A C + C D = A D$
$\Rightarrow C D = 2 b - (a + b) = b - a$
Now, $CE = C D + D E = b - 2 a$