Answer:
Explanation:
1. In order to do this question you have to use the Pythagorean Theorem, which states that for any right triangle with legs a and b, and hypotenuse c (the longer side), a^2+b^2 = c^2 (or the sum of the legs squared equals the hypotenuse squared). For these questions, we can plug in our values. Since one of the legs is x, the other is 12, and the hypotenuse is 13, we can use the Pythagorean Theorem in order to get x^2+12^2 = 13^2 (could interchange the 12^2 and the x^2 terms). After simplifying, we get x^2+144 = 169. By subtracting 144 on both sides, we get x^2 = 25, which means x is 5 after taking the square root of both sides (we ignore the negative solution as a side length can never be negative).
2. This question uses the same strategy as the first. In order to find x, we must use the Pythagorean Theorem, which states that the sum of the two legs squared equals the hypotenuse squared. So, when plugging in our values, we get 3^2+4^2 = x^2 (3^2 and 4^2 can be interchanged) in order to get 9+16 = x^2, which yields 25 = x^2. After taking the square root of both sides, we get 5 = x, which means x is 5 (ignore the negative solution as a side length can never be negative).