Answer:
x=13.45
Explanation:
This is a right triangle. We know this because of the little square in the corner that represents a right angle. Therefore, we can use the Pythagorean Theorem.
a^2+b^2=c^2
where a and b are the legs and c is the hypotenuse.
In this triangle, 10 and 9 are the legs, because they form the right angle. x is the hypotenuse, because it is opposite the right angle.
a=10
b=9
c=x
Substitute these values into the equations.
10^2+9^2=x^2
Evaluate the exponents on the left side.
10^2=10*10=100
100+9^2=x^2
9^2=9*9=81
100+81=x^2
Add 100 and 81
181=x^2
Since x is being squared, take the square root of both sides. The square root and the exponent will cancel, and leave x by itself.
√181=√x^2
√181=x
13.4536240471=x
Round to the nearest hundredth. The 3 in the the thousandth place tells us to leave the 5 in the hundredth place as is.
13.45=x
The hypotenuse of the triangle is 13.45