Answer:
[tex]XZ=12\sqrt{2}\ cm[/tex]
Step-by-step explanation:
Pythagorean theorem: In a right triangle with legs a, b and hypotenuse c,
[tex]a^2+b^2=c^2[/tex]
Given: ΔXYZ is right triangle with right angle Y.
Angles YZX and ZXY are 45 degrees.
ZY = YX = 12 cm
Find: XZ
Solution:
By the Pythagorean theorem,
[tex]XZ^2=XY^2+YZ^2\\ \\XZ^2=12^2+12^2\\ \\XZ^2=144+144\\ \\XZ^2=2\cdot 144\\ \\XZ=12\sqrt{2}\ cm[/tex]
The length of the hypotenuse is [tex]12\sqrt{2}[/tex] cm and this can be determined by using the Pythagorean theorem.
Given :
The length of the hypotenuse can be determined by using the Pythagorean theorem. According to this theorem, the square of the longer side is equal to the sum of the square of the shorter sides.
[tex]\rm H^2=P^2+B^2[/tex] ---- (1)
where H is the hypotenuse, B is the base and P is the perpendicular.
Now, put the value of P and B in equation (1).
[tex]\rm (XZ)^2 = (ZY)^2+(YX)^2[/tex]
[tex]\rm (XZ)^2 = (12)^2+(12)^2[/tex]
[tex]\rm (XZ)^2 = 2\times 144[/tex]
[tex]\rm XZ = \sqrt{288}[/tex]
[tex]\rm XZ = 12\sqrt{2}\; cm[/tex]
For more information, refer to the link given below:
https://brainly.com/question/18163189
