A rectangle with sides 1 cm and 15 cm has the same diagonal as a square. What is the length of the side of the square. Give your answer as a surd.

Question

A rectangle with sides 1 cm and 15 cm has the same diagonal as a square.
What is the length of the side of the square.
Give your answer as a surd.

Answer 1

Let d = the length of the diagonal of the rectangle

a² + b² = c²

15² + 1² = c²

225 + 1 = c²

c = √226 

 

Let s = the length of a side of the square

a² + b² = c²

a² + b² = c²

s² + s² = c²

2s² = 226

s² = 113

s = √113 cm