Question

LO=5 and OK=4, find OH and KH.

Answer 1

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Step-by-step explanation:

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.

Answer 2

Answer:

The correct answer is : OH = 1.441 and KH =  0.557.

Step-by-step explanation:

From the ratio of LH/HI = 5/4, we can solve for LH and HI using the fact that LH + HI = LO + OK = 5 + 4 = 9.

LH/HI = 5/4 implies that LH = (5/4)HI and LH + HI = 9 implies that (5/4)HI + HI = 9.

Solving for HI, we get HI = 9/(5/4 + 1) = 36/13, and LH = (5/4)HI = 45/13.

Now we can use the Pythagorean theorem to find the lengths of the sides of triangle LKI as follows:

LK^2 = LO^2 + OK^2 = 5^2 + 4^2 = 41

KI^2 = LK^2 - LI^2 = LK^2 - (LH + HI)^2 = 41 - (45/13 + 36/13)^2 = 41 - (81/13)^2

KI = (13/√41)√(41 - (81/13)^2)

Using the area formula for triangle LKH, we can solve for KH:

Area(LKH) = (1/2) * LK * KH = (1/2) * LH * OH

Substituting the known values, we get:

(1/2) * 9 * KH = (1/2) * (45/13) * OH

KH = (5/13) OH

Now we can use the Pythagorean theorem to find OH:

OH^2 = OK^2 - KH^2 = 4^2 - [(5/13) OH]^2

OH^2 + (25/169) OH^2 = 16

OH^2 = 16/(1 + 25/169) = 16/(194/169) = 208/97

OH = √(208/97)

Therefore, OH ≈ 1.441 and KH = (5/13)OH ≈ 0.557.

To learn more about pythagorean triples, visit:

https://brainly.in/question/54173046

To learn more about triangles, visit:

https://brainly.in/question/54231692

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