Question

A sail is in the form of a right triangle that is four times as high as it is wide. The sail is made from 32 square meters of material.

Answer 1

im guessing you have to find the height andd the width of the sail?

Answer 2

just the height

Answer 3

Ok, so if the height is 4 times the width, it takes 4 widths to equal 1 height, so h = 4w. We will use w instead of b for the base, ok?

Answer 4

The formula for the area of a triangle is A = 1/2 * w * h. We know the area is 32, and we have a direct relationship between the width and the height. So we can substitute in what we know now. Like this:

Answer 5

yeah

Answer 6

\[32=\frac{ 1 }{ 2 }(w)(4w)\]

Answer 7

We can now solve for w. Then from that we can find the height.

Answer 8

multiply both sides by 2 to get rid of the fraction.

Answer 9

only find the height

Answer 10

I know we only need the height, but you can't find the height without finding the width. So bear with me here.

Answer 11

ok

Answer 12

When you multiply both sides by 2, you get this:\[64=4w ^{2}\]

Answer 13

Divide both sides by 4 to get \[16=w ^{2}\]now what is w?

Answer 14

4

Answer 15

Good! Now remember that we said the height was 4 times the width. Well the width is 4, so what is the height? h = 4w, so h = 4(4).