Answer:
Length of hypotenuse [tex]12\sqrt2[/tex] cm.
Step-by-step explanation:
We are given with a right angled triangle which has angles 45°-45°-90° and sides as 12 cm each.
Following labeling of dimensions is provided:
[tex]\angle XYZ = 90^\circ\\\angle YZX = 45^\circ\\\angle ZXY = 45^\circ[/tex]
Sides:
ZY = 12 cm
YX = 12 cm
Please refer to the image attached as well.
To find: The hypotenuse, XZ = ?
It is well known that if the triangle is a right angled triangle, the pythagorean theorem holds well. As per the theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Height}^{2}\\[/tex]
Here, Base is ZY = 12 cm
Height, YZ = 12 cm
And Hypotenuse XZ is to be calculated.
Putting the values:
[tex]XZ^2=12^2+12^2\\\Rightarrow XZ^2=144+144\\\Rightarrow XZ=\sqrt{144+144}\\\Rightarrow XZ=\sqrt{288}\\\Rightarrow XZ=12\sqrt{2}\ cm[/tex]
So, the answer is Hypotenuse, XZ = [tex]12\sqrt{2}\ cm[/tex].
