Question

Which triangle's unknown side length measures units?

1) A right triangle with a side length of 5 and hypotenuse with length √74
2) A right triangle with a side length of √18 and hypotenuse with length 5
3) A right triangle with a side length of √6 and hypotenuse with length √43
4) A right triangle with a side length of √2 and hypotenuse of 4

Answer 1

To determine which triangle has an unknown side length of a certain number of units, we can use the Pythagorean theorem. By applying the theorem to each given triangle, we can calculate the length of the missing side and compare it to the given unit measurement. The first triangle has a missing side length of 7 units, the second triangle has a missing side length of sqrt(7) units, the third triangle has a missing side length of sqrt(37) units,

Step-by-step explanation:

To determine which triangle's unknown side length measures a certain number of units, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Using this theorem, we can calculate the length of each triangle's hypotenuse and compare it to the given unit measurement.

1. The first triangle has a side length of 5 and a hypotenuse of sqrt(74). Using the Pythagorean theorem, we can find the missing leg length:
   a^2 + b^2 = c^2
   5^2 + b^2 = (sqrt(74))^2
   25 + b^2 = 74
   b^2 = 74 - 25
   b^2 = 49
   b = sqrt(49)
   b = 7
2. The second triangle has a side length of sqrt(18) and a hypotenuse of 5. Using the Pythagorean theorem again, we can find the missing leg length:
   a^2 + b^2 = c^2
   (sqrt(18))^2 + b^2 = 5^2
   18 + b^2 = 25
   b^2 = 25 - 18
   b^2 = 7
   b = sqrt(7)
3. The third triangle has a side length of sqrt(6) and a hypotenuse of sqrt(43). Applying the Pythagorean theorem:
   a^2 + b^2 = c^2
   (sqrt(6))^2 + b^2 = (sqrt(43))^2
   6 + b^2 = 43
   b^2 = 43 - 6
   b^2 = 37
   b = sqrt(37)
4. The fourth triangle has a side length of sqrt(2) and a hypotenuse of 4. Using the Pythagorean theorem once again:
   a^2 + b^2 = c^2
   (sqrt(2))^2 + b^2 = 4^2
   2 + b^2 = 16
   b^2 = 16 - 2
   b^2 = 14
   b = sqrt(14)

Comparing the lengths of the missing sides, we can determine which triangle's unknown side length measures a certain number of units. The missing side length in the first triangle measures 7 units, in the second triangle measures sqrt(7) units, in the third triangle measures sqrt(37) units, and in the fourth triangle measures sqrt(14) units.