Question

akiyo is designing a bird house with a symmetrical roof, as shown in the diagram. what is the total width of the bird house? select one: a. 17.6 cm b. 19.2 cm c. 19.9 cm d. 21.3 cm

Explanation:

Step1: Apply Pythagorean theorem

Let the base - half of the triangle be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 16.2$ cm (hypotenuse) and $a = 12.8$ cm (height). So $x=\sqrt{16.2^{2}-12.8^{2}}$.
\[

$$\begin{align*} x&=\sqrt{(16.2 + 12.8)(16.2-12.8)}\\ &=\sqrt{(29)(3.4)}\\ &=\sqrt{98.6}\\ &\approx9.93 \end{align*}$$

\]

Step2: Calculate total width

Since the roof is symmetrical, the total width of the bird - house is $2x$. So the total width $W = 2x\approx2\times9.93 = 19.86\approx19.9$ cm.

Answer:

C. 19.9 cm