Question

Consider quadrilateral EFGH.

Quadrilateral E F G H is shown. Sides F G and E H are parallel. Angles E and H are congruent. The length of E F is 4 n minus 4, the length of F G is 3 n + 3, and the length of G H is 2 n + 6.

What is the length of line segment GH?

5 units
7 units
16 units
24 units

Answer 1

Given:

In quadrilateral EFGH, $FG\parallel EH,\angleE\cong \angle H,EF=4n-4,FG=3n+3, GH=2n+6$

To find:

The length of segment GH.

Solution:

Draw a figure according to the given information as shown below.

In quadrilateral EFGH, $FG\parallel EH,\angleE\cong \angle H$, it means the quadrilateral EFGH is an isosceles quadrilateral because base angles are equal.

Now, quadrilateral EFGH is an isosceles quadrilateral, so the sides EF and GH are equal.

$EF=GH$

$4n-4=2n+6$

$4n-2n=4+6$

$2n=10$

Divide both sides by 2.

$n=\dfrac{10}{2}$

$n=5$

Now,

$GH=2n+6$

$GH=2(5)+6$

$GH=10+6$

$GH=16$

Therefore, the correct option is C.

Answer 2

Answer:

the answer is C

Step-by-step explanation:

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