Question

Find the missing lengths.

LK=16 and LI=20, find LH and OH.

Answer 1

QUESTION 1

From Pythagoras Theorem,

`|KI|^2+|KL|^2=|LI|^2`

`|KI|^2+16^2=20^2`

`|KI|^2+256=400`

`|KI|^2=400-256`

`|KI|^2=144`

`|KI|=√(144)`

`|KI|=12`

Let
`HI=x`, then
`LH=20-x`

From ΔHKI,

`x^2+|HK|^2=12^2`

`\Rightarrow |HK|^2=144-x^2..(1)`

From ΔHKL,

`|HK|^2+(20-x)^2=16^2`

`\Rightarrow |HK|^2=256-(20-x)^2`

`\Rightarrow |HK|^2=-x^2+40x-144...(2)`

Solving equation (1) and (2) gives

`144-x^2=-x^2+40x-144`

`40x=288`

`x=(36)/(5)`

`|LH|=20-(36)/(5) =(64)/(5)=12.8 units`

QUESTION 2

ΔLKI is similar to ΔOHL

`(|OH|)/(|KI|)=(|LI|)/(|LH|)`

`(|OH|)/(12)=((64)/(5) )/(20)`

`(|OH|)/(12)=(16)/(25)`

`|OH|=(16)/(25)* 12`

`|OH|=(192)/(25)=7.68units`