Question

What is the length of Line BC?

Answer 1

ANSWER:

10

The length of line BC is 10.

EXPLANATION:

Triangle ABC is four times the area of triangle AYX.

Area of triangle ABC = 4 × Area of triangle AYZ

This is as:

30 = 4 × 7.5

THEREFORE:

The length of line BC must be twice of the length of line XY.

BC = 2 × XY

BC = 2 × 5

BC = 10

Answer 2

The length of Line BC is 10

What is a triangle?

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

What are similar triangles?

Triangles having the same corresponding angles measures and proportional side lengths are called similar triangles.

How to find the length of the line BC?

Considering Δ AXY    and    ΔABC

                      ∠AXY       =      ∠ACB  (corresponding angles are equal)

                       ∠AYX       =      ∠ABC   (corresponding angles are equal)

                       ∠A is common in both the triangles

∴ We can say the triangles are similar .

Now, let H be the height of ΔABC and h be the height of ΔAYX

So, we can say,  $\frac{XY}{BC} = \frac{h}{H}$

• Now, we know that area of the triangle can be found with the help of the formula (1/2)x(base)x(height)

So,   $\frac{AYX}{ABC} = \frac{7.5}{30}$

⇒    ${\frac{\frac{1}{2} (XY) h }{\frac{1}{2}(BC) H } = \frac{1}{4}$

Now, substituting XY = 5 and  $\frac{XY}{BC} = \frac{h}{H}$  in the above equation, we get

$\frac{25}{BC^{2} } = \frac{1}{4}$

⇒ BC² = 100

⇒ BC = ± 10

Since BC is the length , so it cannot be negative.

So, the negative value is rejected.

∴  BC = 10

Option B is correct.

Find more about "Similar Triangles" here: https://brainly.com/question/2644832

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