Question

What is the length of side BC of the triangle?

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units

What is the value of x?



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x=

What is the value of x?



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x =

Answer 1

answer is attached below

Answer 2

Answer with explanation:

Ques 1)

We are given:

m∠B=m∠C

As we know that sides opposite to equal angles are equal.

Hence,

Length of AC=Length of AB.

i.e. x+8=2x-1

i.e. 2x-x=8+1

i.e. x=9

Also, the length of side BC is:

3x-3=3×9-3

= 27-3

= 24 units.

The value of x is: 9

Length of BC is: 24 units.

Ques 2)

As we could see that all the three angles of a triangle are equal.

Hence,

The sides opposite to equal angle are equal.

i.e.

6x-3=3x+6

i.e. 6x-3x=6+3

i.e. 3x=9

i.e. x=3

Now the length of side of BC is: 5x=5×3=15 units.

Hence,

Value of x=3

Length of BC=15 units.

Ques 3)

All the three sides of a triangle are equal.

That means:

all the three angles of a triangle are also equal.

Hence, all the angles be (7x+4)°

As we know that the sum of all the three angles of a triangle is 180 degree.

Hence,

`7x+4+7x+7x+4=180\\\\\\21x+12=180\\\\\21x=168\\\\x=8`

Hence, the value of x=8