Question

if one longest side of a right angle triangle is 7cm then find the other two sides

Answer 1

Let one side be x

Then the other side will be,

x + 7 + other side = 180

Therefore, other side = 180 - x - 7 = 173 - x

Using Pythagoras theorem,

ie sum of squares of the legs = square of hypotenuse

In a right angled triangle, the longest side is the hypotenuse.

Therefore, hypotenuse = 7cm

Then,

x^2 + (173 - x) ^2 = 7^2........(Pythagoras Theorem)

x^2 + 173^2 + x^2 - 2*173*x = 49.....(expanding (173 - x) ^2 using the identity (a-b) ^2 = a^2 +b^2 - 2ab)

2x^2 + 29929 - 346x = 49

2x^2 + 29929 - 49 - 346x = 0

2x^2 + 29880 - 346x = 0

x^2 - 173x + 14940 = 0

Now u just have prime factorise the above equation to get the value of x.

Then one side will be x and the other side will be 173 - x

Hope this helps...!
#Cheers