Question

Find the missing lengths.
LK=15 and KH=9, find KI and HI.

Answer 1

QUESTION 1

From Pythagoras Theorem;

`|LH|^2+|KH|^2=|LK|^2`

`\Rightarrow |LH|^2+9^2=15^2`

`\Rightarrow |LH|^2+81=225`

`\Rightarrow |LH|^2=225-81`

`\Rightarrow |LH|^2=144`

`\Rightarrow |LH|=√(144)`

`\Rightarrow |LH|=12`

Let
`|HI|=x`

Then,
`|LI|=12+x`

From ΔKLI,

`|KI|^2+15^2=(12+x)^2`

`|KI|^2+225=x^2+24x+144`

`|KI|^2=x^2+24x+144-225`

`|KI|^2=x^2+24x-81...(1)`

From ΔHKI,

`|KI|^2=x^2+9^2`

`|KI|^2=x^2+81...(2)`

Solving equation (1) and (2) simultaneously, we have;

`x^2+81=x^2+24x-81...(1)`

`81+81=24x`

`24x=162`

`x=(27)/(4)=6.75`

`\therefore |HI|=6.75`

QUESTION 2

Using equation (2)

`|KI|^2=6.75^2+81`

`|KI|^2=126.5625`

`|KI|=√(126.5625)`

`|KI|=11.25`