Question

Consider two triangles with side lengths √8, √32, and √40.

Answer 1

Using the Pythagorean Theorem, the approximate values for x and y are given as follows:

c. x = 5.66, y = 8.

What is the Pythagorean Theorem?

The Pythagorean Theorem relates the length of the legs $l_1$ and $l_2$ of a right triangle with the length of the hypotenuse h, according to the following equation:

$h^2 = l_1^2 + l_2^2$

From the triangle to the right, we have that:

• The sides are x and $\sqrt{8}$.

• The hypotenuse is of $\sqrt{40}$.

Hence:

$x^2 + (\sqrt{8})^2 = (\sqrt{40})^2$

x² + 8 = 40

x² = 32

x = sqrt(32)

x = 5.66.

From the triangle to the right, we have that:

• The sides are both of $\sqrt{32}$.

• The hypotenuse is of y.

Hence:

$y^2 = (\sqrt{32})^2 + (\sqrt{32})^2$

y² = 32 + 32

y² = 64

y = sqrt(64)

y = 8.

Hence option c is correct.

More can be learned about the Pythagorean Theorem at brainly.com/question/654982

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