Answer:
The length of KH is 6 units and OH is 6.3 units.
Step-by-step explanation:
Given the figure with lengths LO=5 and OK=4. we have to find the length of OH and KH.
In ΔLOH
By Pythagoras theorem
[tex]LH^2=LO^2+OH^2\\\\LH^2=5^2+OH^2[/tex] → (1)
In ΔKOH,
[tex]KH^2=OH^2+OK^2\\\\KH^2=OH^2+4^2[/tex] → (2)
In ΔKHL,
[tex]KL^2=LH^2+KH^2[/tex]
Using eq (1) and (2), we get
[tex]KL^2=5^2+OH^2+OH^2+4^2[/tex]
[tex]9^2=25+2OH^2+16[/tex]
⇒ [tex]2OH^2=81-25-16=40[/tex]
⇒ [tex]OH=\sqrt{20}=6.324\sim6.3units.[/tex]
Put the above value in eq 2, we get
[tex]KH^2=20+4^2=36[/tex]
⇒ KH=6 units.
To solve this question, we would be using Pythagoras Theorem. From the diagram, we know that LO = 5 and OK = 4. Also, we can see that KO + OL = KL = 4 + 5 = 9. We are then asked to find the length of OH and KH.
LH² = LO² + OH²
LH² = 5² + OH².........................we take this as equation 1
KH² = KO² + OH²
KH² = 4² + OH²...................we take this as equation 2
KL² = KH² + LH²
Now, if we substitute the equations 1 and 2 into the last one we have noe, we would easily factorize the expression. And thus
KL = 4² + OH² + 5² + OH²
9² = 16 + OH² + 25 + OH²
81 = 41 + 2OH²
2OH² = 81 - 41
2OH² = 40
OH² = 40/2
OH² = 20
OH = √20
OH = 4.47
Again, remember that KH² = KO² + OH², so
KH² = 4² + 4.47²
KH² = 16 + 20
KH² = 36
KH = √36
KH = 6
For more on pythagoras triangles, see https://brainly.com/question/12146092
