If IJ=16 and JK=9, what is the length of HK⎯⎯⎯⎯⎯⎯?
The figure shows right triangle K H I with altitude H J to hypotenuse K I.
A. HK = 20
B. HK = 15
C. HK = 25
D. HK = 12
please help explain this to me thank you.
the two triangles formed by HJ are similar to the original triangle
... so the ratios of corresponding sides are the same
HK / JK = KI / HK
(HK) ^2 = 25 * 9
Hey there! Let's calculate the length of HK together.
Given that IJ = 16 and JK = 9, we can use the Pythagorean Theorem to find the length of HK. 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 other two sides.
So let's calculate it:
IJ^2 + JK^2 = HK^2
16^2 + 9^2 = HK^2
256 + 81 = HK^2
337 = HK^2
Now, we need to find the square root of 337 to get the length of HK:
√337 ≈ 18.357
Since we're looking for an answer choice that's closest to the actual value, the correct option would be:
A. HK = 20
Hope that helps!
To find the length of HK, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, IJ is perpendicular to HK, so it forms a right angle at J. Therefore, triangle KHI is a right triangle.
From the given information, we have IJ = 16 and JK = 9.
Let's assume the length of HK is x.
According to the Pythagorean Theorem, we have:
IJ^2 + JK^2 = HK^2
Substituting the given values, we get:
16^2 + 9^2 = x^2
Simplifying the equation:
256 + 81 = x^2
337 = x^2
To find x, we take the square root of both sides:
√337 = √(x^2)
x ≈ 18.36
Therefore, the length of HK is approximately 18.36.
None of the provided answer choices match this value. It is possible that there is a mistake or typo in the question or answer choices.
To find the length of HK, we can use the Pythagorean theorem, which 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 other sides.
In this given problem, we are given IJ = 16 and JK = 9. We need to find HK.
First, let's label the length of HK as x. Using the Pythagorean theorem, we have:
(HJ)^2 + (JK)^2 = (HK)^2
Substituting the given values, we get:
16^2 + 9^2 = x^2
Simplifying this equation:
256 + 81 = x^2
337 = x^2
Now, we need to find the value of x. Let's take the square root of both sides:
√337 = √(x^2)
√337 = x
Using a calculator, we find that √337 is approximately 18.36.
Therefore, the length of HK, rounded to the nearest whole number, is 18.
None of the answer choices listed in the question match the calculated value of HK. So, the correct answer is not given.