Question

In a right-angled triangle, the longest side is 1 cm longer than the middle side and the middle side is 49 cm longer than the shortest side. Calculate the length of the shortest side?​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Length of the shortest sides 11 cm

Step-by-step explanation:

Concept used:

Pythagoras theorem:

In a right angled square on the hypotenuse is equal to sum of the squares on the other two sides.

Let the sides of the right angled triangle be x, y and z with x<y<z

As per given data,

z=y+1.......(1)

y=x+49......(2)

using (2) in (1)

z=x+50

By pythagoras theorem,

$\pi x^2+y^2=z^2\\\\x^2+(x+49)^2=(x+50)^2\\\\x^2+[(x+50)-1]^2=(x+50)^2\\\\x^2+(x+50)^2+1^2-2(x+50)=(x+50)^2\\\\x^2+1-2x-100=0\\\\x^2-2x-99=0\\\\(x-11)(x+9)=0\\\\x=11,-9$

But x cannot be negative

x=11 cm