Question

unit 6
triangles
lesson 6
distance and the pythagorean theorem
apply the pythagorean theorem to find the length of the diagonal of the square. round your
answer to the nearest hundredth, if necessary.
(1 point)
8
2.83
4
4.24

Explanation:

Step1: Recall the Pythagorean Theorem

For a right - triangle (the diagonal of a square divides it into two right - triangles), \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the sides of the square and \(c\) is the diagonal. Assume the side length of the square \(a = b=2\) (from the number line, the side length between \(0\) and \(2\)).

Step2: Substitute values into the formula

Substitute \(a = 2\) and \(b = 2\) into \(a^{2}+b^{2}=c^{2}\). We get \(2^{2}+2^{2}=c^{2}\), which is \(4 + 4=c^{2}\), so \(c^{2}=8\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{8}\). Simplify \(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\approx2\times1.414 = 2.828\approx2.83\).

Answer:

\(2.83\)