Question

1. The legs of a right triangle measure 24 feet and 45 feet. what is the length of the hypotenuse?

A. 51ft
B.69ft
C.38.07ft
D.8.31ft

2. Which of these cannot represent the lengths of the sides of a right triangle?
A.3 ft,4 ft,5 ft
B.6 in,8 in,10 in
C.16 cm,63 cm,65 cm
D.8 m,9 m,10 m

Answer 1

The answer is A).51 ft
To solve the problem use the Pythagorean Theorem. There are 3 parts to the Pythagorean Theorem. A (squared)+ B (squared) = C(squared). To "square" a number mutiply to itself. A=24
B=45, C is the Hypotenuse, you want to find out C. A is 24, a leg. B is 45, a leg. A squared is 24*24, 576 feet. B squared is 45*45, 2025 feet. To find C (the hypotenuse), add 576+2025 which is 2601 feet. The answer is **2601 feet**. Sometimes they will only give you 1 leg and the hypotenuse and want you to find the 2nd leg answer.
An example is if they asked " a right triangle has a 24 ft leg and hypotenuse is 2,601 ft. What is the length of the other leg? Still use Pythagorean Theorem. A is 24 ft,
you are looking for B,
you know that C is 2601 ft. So it is (24*24) +X squared=2601 ft. Then
2601-576. The answer is 2025, press square root button and it is 45 ft

Answer 2

1.

so remember
a^2+b^2=c^2

a and b are the legs
c=hypotonuse so
a=24
b=45
subsitute
24^2+45^2=c^2
576+2025=c^2
2601=c^2
square root both sides
51=c

the answer is A. 51 ft


2. just subsitute and solve for ones that are not equal (hypotonuse is greater than either legs)
A. 3^2+4^2=5^2
9+16=25
25=25
correrct

B. 6,8,10
this is a multiplule of the 3,4,5 previoius so this works as well

C.16^2+63^2+65^2
256+3969=4225
4225=4225
correct

D. 8^2+9^2=10^2
64+81=100
145=100
false

the answer is D


ANSWERS:
1. A, 51 ft
2. D, 8,9,10