Question

In the diagram shown, FJ bisects AD BL~=LC. The length of CD is 2 more than the length of LC, and the length of AD is

24. What is the length of AC?

Answer 1

The Length of AC is 17 units.

Explanation:

Given:

BL = LC

AD = 24

AL = LD

AL = LD = half of AD = half of 24 = 12. { FJ bisect AD }

Also,

CD = 2 + LC

To Find:

AC = ?

Solution:

By Addition Property we have

LC + CD = LD ............{ L - C - D }

LC + ( 2 + LC ) = 12 ..........{substituting the given values}

∴ 2(LC) = 12 -2

∴ 2 (LC) = 10

∴
`LC =(10)/(2) \\\\LC = 5\ units\\`

Again, By Addition Property we have

AC = AL + LC ................{ A - L - C }

AC =12 + 5

∴ AC = 17 units

∴ The Length of AC is 17 units.