YZ = √ 5 and XZ = √ 2. Find XY. Answer in simplified radical form.
in the given triangle picture Y vertex is 90 degree.
plz help.
sorry. If Y is the right angle of a right triangle, then the legs are XY and YZ
That makes XZ the hypotenuse, which must be the longest side of the triangle.
So what's the typo?
It’s a right triangle.
To find XY, we can use the Pythagorean Theorem. According to the given information, we have a right triangle with Y as the right angle.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is XY and the other two sides are YZ and XZ.
So, we can set up the equation as follows:
XY^2 = YZ^2 + XZ^2
Substituting the given values, we have:
XY^2 = (√5)^2 + (√2)^2
= 5 + 2
= 7
To get the value of XY, we take the square root of both sides:
XY = √7
Therefore, XY = √7, which is the simplified radical form.