Question

Given: Segment AD is an altitude
Find: BC

Answer 1

BC = 71

Explanation:

12x + 6 = 90

x = 7

5x - 7 + 2x + 29 = 7x + 22

7(7) + 22 = 49 + 22

49 + 22 = 71

BC = 71

Answer 2

`BC=71\text{ units}`

Explanation:

Since AD is an altitude, we know that AD⊥BC by the definition of altitudes.

Then, this means that ∠ADC will be 90° by the definition of perpendicular lines. Therefore:

`12x+6=90`

Solve for x. Subtract 6 from both sides and then divide by 12:

`12x=84\\`

`x=7`

Therefore, the value of x is 7.

BC is the addition of the segments BD and DC. In other words:

`BC=BD+DC`

We already know the equations of BD and DC. Substitute:

`BC=(5x-7)+(2x+29)`

Since we know that the value of x is 7, substitute 7 for x and evaluate for BC:

`BC=(5(7)-7)+(2(7)+29))`

Evaluate:

`BC=(35-7)+(14+29)`

Evaluate:

`BC=28+43=71`

Therefore, the value of BC is 71 units.