Question

The diagonal of a square photograph measures 10 inches. Find the length of one of its sides. Give the exact answer and then an approximation to two decimal places.

Answer 1

A square is made up of 4 angles, each equaling 90 degrees, for a total of 360 degrees. A diagonal would cut through the square from one corner to another on the opposite side, cutting 2 of the 90-degree angles in half (45 each) and leaving the other two 90-degree angles untouched. This makes a 45-45-90 triangle. The diagonal is the hypotenuse and is 10 inches, which was given. In all 45-45-90 triangles, the hypotenuse=

`x √(2)`
and the other two sides= x. Since

`x √(2)`
is equal to 10, then x= 10 divided by

`√(2)`
which is 7.07.