Question

In right triangle RST,right angled at T,if RS=50 cm and RT is as large as ST find the length of ST ( in complete centemetre)

Answer 1

In a right triangle side opposite to right angle is hypotenuse
The square of two sides are equal to the square of pytogorean side
According to the Question RT=ST
Therefore :50^2=Rt^2+St^2
=2500 = Rt^2 +St^2
And according to the Question Rt^2=St^2
Therefore =2500/2=1250 =Rt^2=St^2
Rt=St=35.36

Answer 2

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Here is the solution:

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Given that ΔRST is a right angle. RS = 50 and RT = ST

Define x:

Let RT = ST = x

Solve x:

Using Pythagoras' theorem

a² + b² = c²

x² + x² = 50²

2x² =2500

x² = 2500 ÷ 2 = 1250

x  = √1250

x = 25√2 ( in radical form)

x = 35.36 ≈ 35 cm (in nearest cm)

Answer: The length of ST is 35 cm