Question

given the triangle below, what is the length of the hypotenuse?
image of a right triangle with horizontal leg 4 cm, vertical leg 2 cm, and right - angle symbol
a 20 cm
b 12 cm
c $sqrt{12}$ cm
d $sqrt{20}$ cm

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, the Pythagorean theorem states that \(c^{2}=a^{2}+b^{2}\), where \(c\) is the length of the hypotenuse and \(a\) and \(b\) are the lengths of the other two sides.
Here, \(a = 4\space\text{cm}\) and \(b=2\space\text{cm}\).

Step2: Substitute values into the formula

Substitute \(a = 4\) and \(b = 2\) into the formula \(c^{2}=a^{2}+b^{2}\).
We get \(c^{2}=4^{2}+2^{2}\).
Calculate \(4^{2}=16\) and \(2^{2} = 4\). Then \(c^{2}=16 + 4=20\).

Step3: Solve for \(c\)

To find \(c\), take the square root of both sides of the equation \(c^{2}=20\). So \(c=\sqrt{20}\space\text{cm}\) (since length cannot be negative, we take the positive square root).

Answer:

D. \(\sqrt{20}\space\text{cm}\)