Question

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Answer 1

The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132. Lara wrote the following step to find the length of the unknown leg:

Length of the unknown leg = 1572 − 1322 = 24,649 − 17,424 = 7,225 units

Which statement best explains whether Lara's step is correct or incorrect?

It is correct because the length of the unknown side is the difference of the lengths of the sides.
It is correct because the length of the unknown side is the difference of the squares of the sides.
It is incorrect because the length of the unknown side is the square root of 42,073.
It is incorrect because the length of the unknown side is the square root of 7,225.

Answer 2

@jabez177

Answer 3

@rebeccaxhawaii

Answer 4

you should use an ^ to show an exponent:
157^2 − 132^2 = 24,649 − 17,424 = 7,225 units

Answer 5

do you know the Pythagorean theorem ? can you write it down ?

Answer 6

no...

Answer 7

can you look it up. It is very famous (the one formula you should remember)

Answer 8

its about triangles

Answer 9

yes, it is about right triangles (triangles with a 90 degree angle)

Answer 10

its A^2 + B^2=C^2

Answer 11

yes, and the A and B are the *legs* and C is the hypotenuse (longest side)
we don't really care which leg is A and which is B, but it's important that C is the name for the longest side.

Answer 12

ok...

Answer 13

now you have to "use" the equation

when they say
The length of the hypotenuse of a right triangle is 157 units.

which letter in
A^2 + B^2 = C^2
is the 157
any idea ?

Answer 14

C

Answer 15

yes, C is the hypotenuse.
if they tell us the hypotenuse is 157, then we replace the C with 157, like this
A^2 + B^2 = 157^2

Answer 16

oh ok...

Answer 17

next,
The length of one leg of the triangle is 132

we have a choice, both A and B are "legs"
it does not matter which we pick, so let's replace B with 132

A^2 + 132^2 = 157^2

Answer 18

if we want to find A, we have to do some algebra. we add -132^2 to both sides like this:
A^2 + 132^2 - 132^2 = 157^2 - 132^2

on the left side, something minus itself is 0. (that means 132^2 - 132^2 =0)
we get
A^2 + 0 = 157^2 - 132^2

Answer 19

A^2 + 0 is A^2 (adding 0 does not change a value)

so you have
A^2 = 157^2 - 132^2

you will need a calculator to figure out 157^2 and 132^2

Answer 20

24649 and 17424

Answer 21

@phi

Answer 22

yes, so you found
A^2 = 24649-17424
if we simplify that we get
A^2 = 7225

Answer 23

now you have to pay attention to details.
we have found that
A^2 = 7225
but the length of the leg is A (not A^2)
to get A, we "take the square root" of both sides
\[ \sqrt{A^2}= \sqrt{7225} \]
\[ A = \sqrt{7225} \]
you can use a calculator to find what A is

Answer 24

can you answer the question now ?

Answer 25

85!

Answer 26

so the answer is D! @phi

Answer 27

yes