Question

В прямокутному трикутнику KLM (кут KLM=90°) проведено висоту LN. LN=12 см; NM=16см. Знайти катети та гіпотенузу трикутника KLM.​

Answer 1

Ответ:

25 см,  20 см,  15 см.

Объяснение:

Дано: ΔKLM,  ∠KLM=90°, LN - висота,  LN=12 см; NM=16 см.

КM - ? KL - ?  KM - ?

Нехай KN=x см, тоді за теоремою LN=√(KN*MN)

144=16x;  x=9.  KN=9 см.  КМ=9+16=25 см.

LM=20 cм, тому що ΔLMN - єгипетський, сторони кратні 3, 4, 5.

За теоремеою Піфагора

KL=√(KM²-LM²)=√(625-400)=√225=15 см.

Answer 2

Given Information:

We are given a right triangle KLM, where angle KLM is 90 degrees. A height LN is drawn in the triangle, with LN measuring 12 cm and NM measuring 16 cm. We need to find the lengths of the legs (cateti) and the hypotenuse of triangle KLM.

Solution:

To find the lengths of the legs and the hypotenuse of triangle KLM, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

Let's denote the length of KL as a, and the length of KM as b. The length of LN is given as 12 cm, and the length of NM is given as 16 cm.

Using the Pythagorean theorem, we can write the following equation:

a^2 + b^2 = c^2

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Substituting the given values, we have:

a^2 + 12^2 = 16^2

Simplifying the equation:

a^2 + 144 = 256

Subtracting 144 from both sides:

a^2 = 112

Taking the square root of both sides:

a = √112

Simplifying the square root:

a ≈ 10.583

So, the length of KL (one of the legs) is approximately 10.583 cm.

To find the length of KM (the other leg), we can use the fact that the sum of the lengths of the legs is equal to the length of the hypotenuse. Therefore:

a + b = c

Substituting the values we know:

10.583 + b = 16

Subtracting 10.583 from both sides:

b = 16 - 10.583

Simplifying:

b ≈ 5.417

So, the length of KM (the other leg) is approximately 5.417 cm.

Finally, to find the length of the hypotenuse c, we can substitute the values of a and b into the Pythagorean theorem:

c^2 = a^2 + b^2

c^2 = 10.583^2 + 5.417^2

c^2 ≈ 111.833 + 29.417

c^2 ≈ 141.25

Taking the square root of both sides:

c ≈ √141.25

Simplifying the square root:

c ≈ 11.88

So, the length of the hypotenuse KL