A right angled triangle has two shorter sides and one is twice as long as the other.

Question

 The hypotenuse is 25cm long. What are the lengths of the 2 shorter sides?

Answer 1

Hello again, Sarah,

The Pythagorean Theorem states the following: 

a^2 + b^2 = c^2 

Make one side of the triangle x 
Make the second side of the triangle 2x 

Now, you can plug the values into the equation,  right? 

x^2 + 2x^2 = 25^2 or 625  

3x^2 = 625

Divide each side by 3 and you are left with: 

x^2 =  208.33

Now, take the square root of 208.33

x =  14.43

That is the shorter side. The longer side is twice that value: Therefore, 14.43 x 2 = 28.86 14.43 is one side of the triangle. The other is that same value times two. Therefore, the sides of your triangle are: 14.43 Shorter side 28.86 Longer side

Answer 2

x^2 + (2x)^2 = 25^2

 

x^2 + 4x^2 = 625

 

5x^2 = 625

 

x^2 = 125

 

x = sqrt(125) = 5*Sqrt(5)

 

 

The shorter side is 5*sqrt(5)

THe longer side is 10*Sqrt(5)