To calculate the perimeter, sum all of the edges' lengths.
A
a
sqrt(27)+sqrt(72)
B
b
Exact answer: 15+sqrt(27)+sqrt(72)cm^2
Approximate answer: 20.52 cm^2
C
c
Exact answer: 15+sqrt(27)+sqrt(72) cm
Approximate answer: 28.68 cm
Practice makes perfect
a
We want to find the measure of the triangle's third side. We can determine it by adding the two sides labeled x and y in the diagram below.
The sides we labeled, x and y, are both legs of right triangles. Since we know the hypotenuse and second leg in each of these, we can calculate x and y using the Pythagorean Theorem.
When we know the value of x and y, we can determine the unknown side of the original triangle.
b
We also want to find the triangle's area. Since the dashed line is drawn from a vertex and is perpendicular to the side whose length we just determined, we know that these make up the triangle's height and base, respectively. We have enough information to calculate the area.
<listcircle icon="c">Since we know all the sides of the triangle, we have enough information to calculate the perimeter.</listc.ircle>
P&=6+9+sqrt(27)+sqrt(72)cm
& ⇓
P&=15+sqrt(27)+sqrt(72) cm
We also need to find the approximate value of the perimeter.
