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Temka [501]
4 years ago
15

Please help!!! worth 10pts!!!

Mathematics
1 answer:
ser-zykov [4K]4 years ago
8 0

Answer:

third side is 2√33

Step-by-step 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 <u>2√33</u>

Hope this helps!

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