A triangle has a 13-inch side, a 14-inch side, and a 15-inch side. To the nearest tenth
of an inch, how long is the median drawn to the 14-inch side?
I just got the answer 14 is that right? I formed a parallelogram and added the vector lengths and multiplied it by 1/2.
Well, to find the length of the median, we can use the formula:
Median = (1/2) * √(2a^2 + 2b^2 - c^2)
where a, b, and c are the lengths of the sides of the triangle.
In this case, let's call the sides a = 13, b = 14, and c = 15. Plugging these values into the formula:
Median = (1/2) * √(2(13^2) + 2(14^2) - 15^2)
Calculating this, we find that the length of the median is approximately 13.3 inches to the nearest tenth.
So, the median drawn to the 14-inch side is about 13.3 inches. But remember, it's important to use a ruler and measure it accurately!
To find the length of the median drawn to the 14-inch side, we need to first determine the length of the other side that this median is connected to.
Using the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this theorem to the triangle with sides measuring 13 inches, 14 inches, and 15 inches:
13 + 14 > 15
14 + 15 > 13
13 + 15 > 14
Since all three inequalities hold true, we can conclude that this is a valid triangle.
The median divides the side it's drawn to into two equal segments. Since the median is drawn to the 14-inch side, it divides this side into two equal lengths: x and x.
To find the length of x, we can use the formula for medians in a triangle, which states that the length of the median drawn to a side is equal to half the length of the side it's drawn to.
Therefore, the length of the median drawn to the 14-inch side is equal to half of 14 inches.
Length of median = 14 / 2 = 7 inches.
So, to the nearest tenth of an inch, the length of the median drawn to the 14-inch side is 7 inches.
To find the length of the median drawn to the 14-inch side, we need to remember that a median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side. In this case, we want to find the median drawn to the 14-inch side of the triangle.
To calculate the length of the median, we can use the formula:
Length of the median = (1/2) × sqrt(2a^2 + 2b^2 - c^2)
Where a, b, and c represent the lengths of the sides of the triangle.
In our case, the sides of the triangle are:
a = 13 inches
b = 14 inches (the side to which we want to draw the median)
c = 15 inches
Plugging in these values into the formula:
Length of the median = (1/2) × sqrt(2 × 13^2 + 2 × 14^2 - 15^2)
Simplifying further:
Length of the median = (1/2) × sqrt(2 × 169 + 2 × 196 - 225)
Length of the median = (1/2) × sqrt(338 + 392 - 225)
Length of the median = (1/2) × sqrt(505)
Taking the square root:
Length of the median ≈ (1/2) × 22.471
Rounding to the nearest tenth of an inch:
Length of the median ≈ 11.2 inches
Therefore, the length of the median drawn to the 14-inch side of the triangle is approximately 11.2 inches.
Nope. You have ignored the triangle inequality.
From the law of cosines, the angle ? between the 13 and 15 sides is
14^2 = 13^2+15^2-2*13*15 cos?
? = 59.5°
So, if we let the short side be
u = 13i
The 15" side is
v = 7.62i + 12.92j
The median m is then
m = (u+v)/2 = (20.62i + 12.92j)/2
= 10.31i + 6.47j
|m| = 12.17
Or, use the handy formula found here:
http://www.cut-the-knot.org/triangle/LengthOfMedian.shtml