Question

using algebra find the value of each variable. 26. triangle with sides 12, 16, 20 and altitude x

Explanation:

Step1: Identify right triangle, find area

First, recognize this is a right triangle with legs 12 and 16. Calculate its area:
$\text{Area} = \frac{1}{2} \times 12 \times 16 = 96$

Step2: Use hypotenuse to solve for $x$

The hypotenuse of the triangle is 20, and $x$ is the altitude to the hypotenuse. Use the area formula with hypotenuse as base:
$\text{Area} = \frac{1}{2} \times 20 \times x$
Substitute the known area:
$96 = \frac{1}{2} \times 20 \times x$

Step3: Solve for $x$

Simplify and isolate $x$:
$96 = 10x$
$x = \frac{96}{10} = 9.6$

Answer:

$x = 9.6$ (or $\frac{48}{5}$)