Question

Use the Pythagorean theorem to find the length of the diagonal of a square that has an area of 289 square inches

Answer 1

Answer:

The answer is approximately 24.041 inches (round to the nearest tenth, hundredth, or thousandth if it is indicated in the instructions.)

Step-by-step explanation:

First, I figured out what the square root of 289 is. The square root of 289 is 17.

Given that this is a square we are dealing with, we can assume that all sides are equal.

So, when you draw a diagonal down the square, it becomes two triangles, one of which we can use the Pythagorean theorem for.

a^2 + b^2 = c^2. Thus, 17^2 + 17^2 = 578. The square root of 578 unfortunately does not come out evenly, so we are left with approximately 24.041 inches.

I hope this helps!

Answer 2

Answer: $17\sqrt{2}$ (exact) or 24.0416 (decimal)

Step-by-step explanation:

find side length

since the area of a square is a = s^2, plug in 289 for a to find the side length

289 = s^2

s = 17

use pythagorean theorem

the Pythagorean theorem says that a^2 + b^2 = c^2 where a and b are perpendicular sides of a triangle, so a and b would be the side length of the square (a=b=17), and c would be the diagonal

so 17^2 + 17^2 = c^2

578  = c^2

c = $17\sqrt{2}$ ≈24.0416

final answer

exact = $17\sqrt{2}$

decimal = 24.0416