Question

Ok so im doing my geometry homework and im very confused. Were doing Triangles

26(A)
24 (B)
X (C)

So I Did:

C²=A²+B²
X²=(26)²+(24)²
X²=676+576
X²=1252
X=

Does 1252 have a square root? if it does can someone please tell me and help me solve this problem because im so confused

Answer 1

X = √1252 = 2√313 ≈ 35.384

Explanation:

Every number has a square root. If the number is not a perfect square, then that square root is irrational. (If the number is negative or complex, the square root is complex.)

Your scientific calculator can tell you what the approximate decimal value of the square root of 1252 is.

You will recognize that it is an even number, and that it is divisible by 4. This means the square root can be simplified a little bit.

`X=√(1252)=√(2^2\cdot 313)=√(2^2)√(313)\\\\X=2√(313)`

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Comment on your numbers

The numbers 24 and 26 suggest that perhaps X has a different value. The triple (5, 12, 13) is a fairly common Pythagorean triple, so we might expect you to be seeing the numbers (10, 24, 26), which are double those values. In the formula c² = a² + b², that would make 26 = c.

What is always true is that the sum of the squares of the sides is equal to the square of the hypotenuse. The designations of a, b, c don't always correspond to sides and hypotenuse in that order. In any given problem, they may be mixed up. Check the diagram.