Question

How could Lynn calculate the length of the diagonal of a square?

A. by multiplying the length of the square times itself
B. by adding the lengths of all four sides of the square
C. by multiplying 1/2 by the length of the base times the height
D. by squaring one side length and doubling the value; then taking the square root of that value

Answer 1

D. by squaring one side length and doubling the value; then taking the square root of that value

Explanation:

Multiplying the length of the square by itself gets you the area of the square, so A is incorrect.

Adding the lengths of all four sides of the square gets you the perimeter of the square, so B is incorrect.

Multiplying 1/2 by the length of the base times the height would get you the area of half of the square, so C is incorrect.

What you need to do is use the Pythagorean theorem:
`a^2 + b^2 = c^2`. This formula means that the legs of a right triangle squared and added together will equal the diagonal side squared. Since the side lengths of a square are all the same, we can simplify the formula into
`2a^2 = c^2`. When we solve that equation for the diagonal, we get
`c = √(2a^2)`, which is what answer D describes. Therefore, D is correct.

Answer 2

D. By doubling one side length and doubling the value; then taking the square root of that value

Explanation:

A square as all its sides equal and all the angles in a square are right angles (90°).

Hence, Pythagoras theorem can be applied since the diagonal is the longest side of a square