If the shortest side of a right triangle is 19, what are the lengths of the other TWO sides that makes the side lengths a Pythagorean triple? HELP ASAP PLZ

180 and 181

Step-by-step explanation:

A pythagorean triple basically refers to numbers that satisfies the pythagorean theorem. This theorem states that the square of the hypotenus (a) of a right angle triangle is equal to the sum of the squares of the other two sides (b and c).

That is;

a² = b² + c²

If the shortest side is 19, the other two sides are 180 and 181.

The hypotenus is the longest side of the right angle triangle.

Check:

181 = 180 + 19

181² = 180² + 19²

32761 = 32400 + 361

32761 = 32761

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt