Question

If BD = 7x-10, BC = 4x-29, and CD = 5x-9, find each value.

Answer 1

BD = BC + CD
7x - 10 = (4x - 29) + (5x - 9)
7x - 10 = 9x - 38
2x = 28
Ans: x = 14
BC = 4x - 29
= 4(14) - 29
= 27
Ans: BC = 27
CD = 5x - 9
= 5(14) - 9
= 61
Ans: CD = 61
BD = 61 + 27
= 88
Ans: BD = 88

Answer 2

`x=14`,
`BD=88`,
`BC=27`,
`CD=61`.

The value of CD is 61 units.

Explanation:

Given information: BD = 7x-10, BC = 4x-29, and CD = 5x-9,

From the given figure it is clear that Points B, C and D collinear. Point C lies on line segment BD.

`BD=BC+CD`

Substitute BD = 7x-10, BC = 4x-29, and CD = 5x-9 in the above equation.

`7x-10=(4x-29)+(5x-9)`

On combining like terms we get

`7x-10=(4x+5x)+(-29-9)`

`7x-10=9x-38`

Add 38 on both sides.

`7x-10+38=9x`

`7x+28=9x`

Subtract 7x from both sides.

`28=9x-7x`

`28=2x`

Divide both sides by 2.

`14=x`

Therefore the value of x is 14.

`BD = x-10=7(14)-10=88`

The value of BD is 88 units.

`BC = 4x-29=4(14)-29=27`

The value of BC is 27 units.

`CD = 5x-9=5(14)-9=61`

The value of CD is 61 units.