Question

Right angled triangle
In right angled triangle XYZ, right angled at Y, XY=10cm, XZ=26cm.

a) According to Pythagoras theorem which statement is true?
i) XY2 = YZ2 + XZ2 ii) XZ2 = XY2 + YZ2 iii) XY + YZ = XZ iv) YZ2 = XY2 + XZ2
b) What is the length of YZ?
i) 16
ii) 24
iii) 36
iv) 18
c) What is the unit digit in the square of 26?
i) 4 ii) 6
iii) 8
iv) 3
d) Identify the largest side.
i) XY ii) YZ
iii) ZX
iv) None of these
e) Which is the largest angle in this triangle?
i) ZY ii) _ZX
iii) 2X iv) ZZ
​

Answer 1

Answer:

Y is right angle.

So, XY and YZ are the arms and XZ is hypotenuse.

a) So, according to pythagoras' theorem, XZ^2 = XY^2 + YZ^2

b) XZ^2 = XY^2 + YZ^2

=> (26)^2 = (10)^2 + YZ^2

=> YZ = √((26)^2 - (10)^2) = √(676 - 100) = 24

c) Unit digit is 6

d)We know that hypotenuse of a right triangle is the largest side. So Largest side = XZ

e) We know, angle opposite to largest side = largest angle. Therefore, largest angle = angle Y (90 degrees)