Because the triangle is a right triangle (a triangle that contains a 90° angle), we can use the Pythagorean Theorem.
Pythagorean Theorem:
a²+b²=c², where a=leg 1, b=leg 2, and c=hypotenuse.
Define variables:
Leg 1=√10km, leg 2=x, and hypotenuse=√15. So, a=√10, b=x, c=√15.
Substitute variables in and solve for undefined variable:
(√10)²+(x)²=(√15)²
Simplify:
10+x²=15
Squares are inverse operations of square roots, so they cancel each other out, or “undo” each other. For example: 10•10=100 and √100=10, so √10²=10. Or, 6•6=36, so √36=6, thus √6²=6.
Solve for x:
Subtract 10 from both side:
x²=15-10
x²=5
Take the square root of x² to both sides so we are left with just x. Again, this works because x•x=x², so √x²=x, thus √x²=x. And, whatever we do to one side, we must do to the other to keep the equation balanced.
√x²=√5
x=√5km
Answer:
Choice A.): x=√5km