Answer:
third side is 2√33
Explanation:
Hi there!
We need to find the third side (hypotenuse, or the side opposite to the right angle) of the triangle, and we're given the measures of the 2 other sides (legs, or the sides make up the right angle)
To find the hypotenuse, we can use Pythagorean theorem, which is given as:
a²+b²=c², where a and b are the legs, and c is the hypotenuse
as stated above, we know that the legs are 7 and √83
substitute them as a and b into the theorem
remember that (√x)²=(√x)(√x)=x
7²+(√83)²=c²
raise all numbers (multiply 7 by itself and multiply √83 by itself)
49+83=c²
add 49 and 83 together
132=c²
take the square root of both sides
√132=c
the question asks for simplest radical form, written as x√y, where x is the square root of a perfect square, and y is what's left after the prefect square is pulled out. For example, 2√3 is √12 (12 is 4*3, and 4 is a perfect square. Recall that √xy is equal to √x*√y. Taking the square root of 4 gives us 2, while taking the square root 3 gives us √3. Multiplying them together makes the number 2√3)
132 is divisible by 4 (the last two digits makes 32, which is divisible by 4). 132/4=33
so 132 is 4*33
pull out 4 from under the radical, take the square root of it, and leave √33 as is
the simplified radical form is 2√33
So the third side is 2√33
Hope this helps!