Question

Solve for both problems a) & b)
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Due within 8 hours

Answer 1

a. triangle STV is NOT a right triangle

b. 9 and 12

Explanation:

a. If triangle STV is a right triangle, according to Pythagoras theorem, c^2 = a^2 + b^2

if c = 14 => 14^2 = 196

if a = 7 and b = 11 => 7^2 + 11^2 = 170

since c^2 is not equal to a^2 + b^2, triangle STV is not a right triangle

b. if hypotenuse, which is c, is 15 => c^2 = 15^2 = 225

since a^2 + b^2 = c^2 => a^2 + b^2 = 225

since c is hypotenuse, a and b must be less than 15

for whole number:

1^2 = 1

2^2 = 4

3^3 = 9

4^2 = 16

5^2 = 25

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

10^2 = 100

11^2 = 121

12^2 = 144

13^2 = 169

14^2 = 196

The only 2 whole number which can add up to 225 is 9 and 12

9^2 + 12^2 = 225

so the legs are 9 and 12 long

Answer 2

• {7, 11, 14} is NOT a right triangle
• {9, 12, 15} is a right triangle

Explanation:

You want to know if sides of lengths {7, 11, 14} make a right triangle, and what integer side lengths make a right triangle with hypotenuse 15.

a) {7, 11, 14}

There are at least two ways you know these lengths do not form a right triangle:

1. The only Pythagorean triples with hypotenuse lengths under 20 units are {3, 4, 5}, {5, 12, 13}, and {8, 15, 17} and their multiples. {7, 11, 14} is not one of them.
2. The only right triangle with a shortest side : longest side ratio of 1 : 2 is the 30°-60°-90° "special" right triangle with sides in the ratio 1 : √3 : 2. The other leg is irrational, which 11 is not.

Side lengths {7, 11, 14} cannot form a right triangle.

b) Hypotenuse 15

As we saw above, any right triangle with a hypotenuse of 15 will be a multiple of the {3, 4, 5} right triangle. Multiplying by 3, we get {9, 12, 15}, so the leg lengths must be 9 and 12.

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Additional comment

As you can see, it is useful to be familiar with a few of the Pythagorean triples (integer lengths that form a right triangle). It is also useful to be familiar with the "special" right triangles that have angles 45°-45°-90° and 30°-60°-90°.