Question

¿cuál es la longitud de la diagonal de un rectángulo cuya base mide 12 centímetros y tiene una altura de 9 centímetros?
a. 15 cm
b. 42 cm
c. 108 cm
d. 225 cm

Explanation:

Step1: Recall Pythagorean theorem

In a rectangle, the diagonal forms a right triangle with the length and width. The Pythagorean theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(c = \sqrt{a^{2}+b^{2}}\). Here, \(a = 12\) cm (base) and \(b = 9\) cm (height).

Step2: Calculate \(a^{2}+b^{2}\)

First, find \(a^{2}\) and \(b^{2}\). \(a^{2}=12^{2}=144\) and \(b^{2}=9^{2} = 81\). Then, \(a^{2}+b^{2}=144 + 81=225\).

Step3: Find the square root

Take the square root of \(225\) to get the length of the diagonal. \(\sqrt{225}=15\) cm.

Answer:

A. 15 cm