Can a right triangle have a leg that is 10 meters long and a hypotenuse that is 10 meters long

Lets see
a and b are legs
c=hypotnuse
a^2+b^2=c^2
10^2+b^2=10^2
100+b^2=100
minus 100 both sides
b^2=0
b=0
false, if you have a leg legnth 0, then they lines are right on top of each other

no cannot

Solutions

To solve this problem we have to use the Pythagorean theorem. You can only use the Pythagorean theorem in Right Triangles. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate c² we have to do α² + β² = c². 

Given 

α² = 10 
c² = 10 

Solve 

α² + β² = c² 
α² (10²) + β² = c² (10²) 
100 + β² = 100 
β² = 100 - 100 = 0 

Simplify 

A right triangle can not have a leg that is 10 meters long and a hypotenuse that is 10 meters long.