Question

pythagorean theorem - worksheet
for each triangle find the missing length. round your answer to the nearest tenth. then find the area and the perimeter.
1.
triangle with hypotenuse 19, base 17, height?
2.
right triangle with leg 5, base 13, hypotenuse?
3.
right triangle with hypotenuse 20, height 10, base?
4.
right triangle with leg 5, base 14, hypotenuse?

Explanation:

Step1: Solve Triangle 1 (Missing Leg)

The Pythagorean theorem is \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse. Here, \(c = 19\), one leg \(a = 17\), find \(b\).
\(b^2 = c^2 - a^2 = 19^2 - 17^2 = 361 - 289 = 72\)
\(b = \sqrt{72} \approx 8.5\)

Step2: Solve Triangle 2 (Missing Hypotenuse)

\(a = 5\), \(b = 13\), find \(c\).
\(c^2 = 5^2 + 13^2 = 25 + 169 = 194\)
\(c = \sqrt{194} \approx 13.9\)

Step3: Solve Triangle 3 (Missing Leg)

\(c = 20\), one leg \(a = 10\), find \(b\).
\(b^2 = 20^2 - 10^2 = 400 - 100 = 300\)
\(b = \sqrt{300} \approx 17.3\)

Step4: Solve Triangle 4 (Missing Hypotenuse)

\(a = 5\), \(b = 14\), find \(c\).
\(c^2 = 5^2 + 14^2 = 25 + 196 = 221\)
\(c = \sqrt{221} \approx 14.9\)

Answer:

1. Missing length: \(\approx 8.5\); Area: \(\frac{1}{2} \times 17 \times 8.5 \approx 72.25\); Perimeter: \(17 + 8.5 + 19 \approx 44.5\)
2. Missing length: \(\approx 13.9\); Area: \(\frac{1}{2} \times 5 \times 13 = 32.5\); Perimeter: \(5 + 13 + 13.9 \approx 31.9\)
3. Missing length: \(\approx 17.3\); Area: \(\frac{1}{2} \times 17.3 \times 10 \approx 86.5\); Perimeter: \(17.3 + 10 + 20 \approx 47.3\)
4. Missing length: \(\approx 14.9\); Area: \(\frac{1}{2} \times 5 \times 14 = 35\); Perimeter: \(5 + 14 + 14.9 \approx 33.9\)