Question

Letry. 14 Chapter 9: Chapter 9 rest Chapter Test

Answer 1

Answer:

h = 7.1 cm

Step-by-step explanation:

To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:

$S = \sqrt{p(p-a)(p-b)(p-c)}$

Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:

$p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm$

So the area of the triangle is:

$S = \sqrt{20(20-15)(20-8)(20-17)}$

$S = 60\ cm^2$

Now, to find the height, we can use the following equation for the area of the triangle:

$S = base * height/2$

The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:

$60 = 17 * h/2$

$h = 120/17$

$h = 7.06\ cm$

Rounding to the nearest tenth, we have h = 7.1 cm