CBSE Class 10 Maths Problems on Pythagoras Theorem

Solution

By Pythagoras theorem, p² = q² + x² … (third side is x)

p² − q² = x² (p + q)(p − q) = x²(p + p − 1) = x² … (p − q = 1) 

x² = 2p − 1 

Solution

Let the shortest side be x, the hypotenuse be 2x + 1 and the third side be 2x − 1.

By Pythagoras theorem,

(2x + 1)² = x² + (2x − 1)²

x² − 8x = 0

x(x − 8) = 0

x = 8 or x = 0 … (side cannot have 0 length) 

Solution

The triangle is a 45-45-90 degree triangle.

So, it is an isosceles triangle.

Hypotenuse² = 2 × other side² = √2 × other side