Question

Find the missing length using the Pythagorean theorem. Show your steps.

Answer 1

4 cm.

Explanation:

The Pythagorean Theorem Is:

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`a^2 + b^2 = c^2\\ \rule{150}{0.5}\\ \text{a, b - measurements of the \textbf{legs} of a \textbf{right triangle.}}\\ \text{c - measurement of the \textbf{hypotenuse} of a \textbf{right triangle.}}\\\\\\ \text{The sums of the squares of the legs of a right triangle is equal to the square of the hypotenuse.}`

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We are given the hypotenuse measurement of 5 cm and a leg measurement of 3 cm.

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`a^2 + 3^2 = 5^2\\ \rule{150}{0.5}\\ a^2 + 9 = 25\\\\ a^2+ 9 - 9 = 25 - 9 \\\\ a^2 = 16\\\\ √(a^2) =√(16)\\\\ \boxed{a = 4}`

The measurement of the missing leg is 4 cm.

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Hope this helps!

Answer 2

4

Explanation:

let unknown side be x

5^2= x^2+3^2

x^2=5^2-3^2

x^2=(5)^2-(3)^2

x^2= 25-9

x^2=16

x= square root of 16

x=4