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Veseljchak [2.6K]
3 years ago
9

What is ​ BC ​ ? Enter your answer in the box. Units An isosceles triangle A B C. Side B C is the base. Sides A B and A C are eq

ual. Sides A B and A C are labeled with single tick marks. Side A B is labeled as 4 x plus 1, side A C is labeled as 2 x plus 23, and side B C is labeled as 3 x minus 8.
Mathematics
1 answer:
GuDViN [60]3 years ago
8 0

Answer:

BC = 25

Step-by-step explanation:

Since AB = AC, then substituting values gives

4x + 1 = 2x + 23 ( subtract 2x from both sides )

2x + 1 = 23 ( subtract 1 from both sides )

2x = 22 ( divide both sides by 2 )

x = 11

Hence

BC = 3x - 8 = (3 × 11) - 8 = 33 - 8 = 25

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Answer:

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Step-by-step explanation:

<u><em>The complete question is</em></u>

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?

step 1

Find the measure of the interior angle

Let

x ---> the measure of the interior angle

y ---> the measure of the exterior angle

Remember that

the sum of the interior and exterior angle in any polygon is equal to 180 degrees

so

x+y=180^o ----> equation A

we have that

the measure of the interior angle is twice the measure of the exterior angle

so

x=2y ----> equation B

substitute equation B in equation A

2y+y=180

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so

x=120^o

That means-----> The figure is a regular hexagon

step 2

Remember that

The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon

Let

b ----> the length side of the hexagon

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b=12/2=6\ units

The perimeter of the hexagon is given by the formula

P=6b

substitute

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