Question

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

Length of the unknown leg= 157^2 - 132^2=24,649 - 17,424= 7,225 units
Which statement best explains whether Lara’s step is correct or incorrect?
A. It is correct because the length of the unknown side is the difference of the lengths of the sides
B. It is correct because the length of the unknown side is the difference of the squares of the sides
C. It is incorrect because the length of the unknown side is the square root of 42,073
D. It is incorrect because the length of the unknown side is the square root of 7,225

Answer 1

The answer is D.

Explanation:

She forgot to find the square root of 7225.

Answer 2

D. It is incorrect because the length of the unknown side is the square root of 7,225

Explanation:

Because it is a right triangle, we can use the Pythagorean theorem

a^2 +b^2 = c^2

where a and b are the legs and c is the hypotenuse

132^2 + b^2 =157^2

17424 +b^2 =24649

Subtract 17424 from each side

17424-17424 +b^2 =24649 - 17424

b^2 =7225

Take the square root of each side

sqrt(b) = sqrt(7225)

b = 85