Question

1. if bd = 7x - 10, bc = 4x - 29, and cd = 5x - 9, find each value. x = bc = cd = bd = 8. if bd = bc, bd = 5x - 26, bc = 2x + 1, and ac = 43, find ab.

Explanation:

Step1: Set up the equation for problem 8

Since $BD = BC$, we set $5x - 26=2x + 1$.
$5x-2x=1 + 26$
$3x=27$
$x = 9$

Step2: Find the length of $BC$

Substitute $x = 9$ into the expression for $BC$. $BC=2x + 1=2\times9+1=19$.

Step3: Find the length of $AB$

We know that $AC = 43$ and $AC=AB + BC$. So $AB=AC - BC$. Substitute $AC = 43$ and $BC = 19$, we get $AB=43-19 = 24$.

Step4: Set up the equation for problem 7

Since $BD=BC + CD$, we have $7x-10=(4x - 29)+(5x - 9)$.
$7x-10=4x-29 + 5x-9$
$7x-10=9x-38$
$9x-7x=38 - 10$
$2x=28$
$x = 14$

Step5: Find the values for problem 7

• $BC=4x-29=4\times14-29=56 - 29=27$
• $CD=5x-9=5\times14-9=70 - 9=61$
• $BD=7x-10=7\times14-10=98 - 10=88$

Answer:

For problem 8: $AB = 24$
For problem 7:
$x = 14$
$BC = 27$
$CD = 61$
$BD = 88$