3 Answers | Add Yours
Two sides of a right triangle are equal to 8 and 10. The third side has to be determined. This side can either be the shortest side, or one that lies between 8 and 10 or the longest side. For each of the three cases, if the length of the unknown side is X, we have:
1. `X^2 + 8^2 = 10^2`
=> `X^2 = 100 - 64`
=> `X^2 = 36`
=> X = 6
X can only take on the value 6 that satisfies the Pythagorean theorem while X is not the longest side.
2. X^2 = 8^2 + 10^2
=> X^2 = 64 + 100
=> X^2 = 164
=> X = `sqrt 164`
There are two values of the length of the third side, 6 and `sqrt 164` .
Rigtht angle triangles can be constructed with 2 configurations using line segments of length 8 and 10.
Case 1. When one side = 8,hypotenuse = 10 and 2nd side = x
8^2 + x^2 = 10^2
x^2 = 100-64 = 36
x = 6
Case 2. When one side 8, other side = 10 and hypotenuse = x
using paythogoras theorem:
x^2 = 8^2 + 10^2
x^2 = 164
x = square root of 164
A right angle triangle cannot exist with line segment of length 8 as hypotenuse as it is shorter than the line the side of length 10.
You have to use paythagoras therum to find the answer.
As 8 is a lower value than 10, it will be the short side, and ten will by the long side (hyptenuse)
so you do x to the power of 2 + 8 to the power of 2 will equal 10 to the power of two. Therefore to find the value of x you do square root of 10 to the power of two minus 8 to the power of 2. Which will give you 6. or you could write it as the square root of 164.
Hope this helps
We’ve answered 330,360 questions. We can answer yours, too.Ask a question