Question

use the figure shown. what is the measure of side a? a =

Explanation:

Step1: Identify right - triangle

Consider right - triangle BDC. Assume each grid square has side - length 1. The vertical side BD has length 3 and the horizontal side DC has length 4.

Step2: Apply Pythagorean theorem

For a right - triangle with legs of lengths $x$ and $y$ and hypotenuse of length $z$, the Pythagorean theorem is $x^{2}+y^{2}=z^{2}$. Here, $x = 3$ and $y = 4$, and $z=a$. So, $a=\sqrt{3^{2}+4^{2}}$.

Step3: Calculate the value of $a$

$a=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

5