Question

A square has sides of length 15. What is the length of the diagonal?
А
14/4
B
15/2
C
16/5
D
12/3

Answer 1

Answer:

15 sqrt(2) =c

Step-by-step explanation:

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

The legs are 15 and the hypotenuse is the diagonal

15^2 + 15^2 = c^2

2 * 15^2 = c^2

Take the square root of each side

sqrt(2 * 15^2 )=sqrt( c^2)

sqrt(2) sqrt(15^2) = c

15 sqrt(2) =c

Answer 2

Answer: 15$\sqrt{2}$ (b)

Step-by-step explanation:

You can separate a square into two different 45-45-90 degree triangles.

Where x = 15, and the diagonal would be the hypotenuse.

So, here you can use the Pythagorean Theorem to find the hypotenuse to use 45-45-90 triangle theorem where they hypotenuse is always x times $\sqrt{2}$

So, the diagonal would be 15$\sqrt{2}$