Question : x, y, and z are the sides of a triangle. If z is the largest side and x2 + y2 > z2, then the triangle is a:
Option 1: Isosceles right angled triangle
Option 2: Acute angled triangle
Option 3: Obtuse angled triangle
Option 4: Right angled triangle
Correct Answer: Acute angled triangle
Solution :
Given: That x, y, and z are the sides of a triangle. If z is the largest side and x
2
+ y
2
> z
2
.
If a triangle's sides are x, y, and z, where side z is the largest side. Then,
The triangle is a right-angled triangle if x
2
+ y
2
= z
2
.
The triangle is an acute-angled triangle if x
2
+ y
2
> z
2
.
The triangle is an obtuse angled triangle if x
2
+ y
2
< z
2
.
In this case, the triangle's sides are x, y, and z, with z being the largest side.
The given condition is x
2
+ y
2
> z
2
.
The above situation satisfies the acute angle triangle criterion. So, the triangle is an acute-angled triangle.
Hence, the correct answer is an acute-angled triangle.
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