Question

What is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vertex A lies above side B C. Angle B and angle C are marked congruent. The length of side A C is labeled as 2 x plus 7. The length of side A B is labeled as 4 x minus 7. The length of side B C is labeled as 4 x.

Answer 1

Answer:

The length of BC = 28 units

Step-by-step explanation:

* In triangle ABC

∵ Angles B and C are congruent

∴ m∠B = m∠C

* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length

∴ AB = AC

∵ AB = 4x - 7

∵ AC = 2x + 7

∴ 4x - 7 = 2x + 7 ⇒ collect like terms

∴ 4x - 2x = 7 + 7

∴ 2x = 14 ⇒ divide both sides by 2

∴ x = 14 ÷ 2 = 7

* Now we can find the length of BC

∵ The length of BC = 4x ⇒ substitute the value of x

∴ The length of BC = 4 × 7 = 28 units