Question

solve for c given that the height of the triangle is 11 centimeters.

Explanation:

Step1: Apply Pythagorean theorem

The right - triangle formed by half of the base, the height and the side has base length $a = \frac{5}{2}$ and height $b = 11$. The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$.

Step2: Substitute values

Substitute $a=\frac{5}{2}$ and $b = 11$ into the formula: $c^{2}=(\frac{5}{2})^{2}+11^{2}=\frac{25}{4}+121=\frac{25 + 484}{4}=\frac{509}{4}$.

Step3: Solve for $c$

Take the square - root of both sides: $c=\sqrt{\frac{509}{4}}=\frac{\sqrt{509}}{2}\approx\frac{22.56}{2}=11.28$ (rounded to two decimal places).

Answer:

$c=\frac{\sqrt{509}}{2}\text{ cm}\approx11.28\text{ cm}$