Question

Consider the hypotenuse of a right triangle with two legs that are two inches and one inch long, respectively. The length of the hypotenuse, in inches, is between which pair of the following fractions?
a 9/4 10/4
b 17/8 18/8
c 14/4 15/4
d ¼ ⅓
e ¾ 5/4

Answer 1

Answer:

b

Step-by-step explanation:

Pythagoras formula for the relation of the side lengths of a right-angled triangle :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90 degree angle). a and b are the "legs".

so, we have here

c² = 1² + 2² = 1 + 4 = 5

c = sqrt(5) = 2.236067977...

so, answer option c is too big (values bigger than 3).

answer options d and e are too small (values smaller than 2).

a

9/4 = 2.25

10/4 = 2.5

this is also too big .

that leaves us with b

17/8 = 2.125

18/8 = 9/4 = 2.25

that is correct