Question

8.

A right triangle shaped sail has an area of 150 square
meters. The base of the sail is 10 less than twice the
ight. Find the base and the height.

Answer 1

The height is 15 meters and the base is 20 meters.

Explanation:

Let's use the formula for the area of a right triangle:

A = (1/2)bh

Where A is the area, b is the base, and h is the height.

We're given that the area is 150 square meters, so we can substitute that in:

150 = (1/2)bh

Next, we're told that the base is 10 less than twice the height. In other words,

b = 2h - 10

We can substitute this expression for b into the equation for the area:

150 = (1/2)(2h - 10)h

Simplifying:

300 = (2h - 10)h

300 = 2h^2 - 10h

2h^2 - 10h - 300 = 0

Dividing both sides by 2:

h^2 - 5h - 150 = 0

Now we can solve for h using the quadratic formula:

h = (-(-5) ± sqrt((-5)^2 - 4(1)(-150))) / 2(1)

h = (5 ± sqrt(625)) / 2

h = (5 ± 25) / 2

We can ignore the negative root (which gives us a negative height), so:

h = 15

Now we can use the expression for b in terms of h to find the base:

b = 2h - 10

b = 2(15) - 10

b = 20

Therefore, the height is 15 meters and the base is 20 meters.

Answer 2

Base=20m height= 15m

Explanation:

The area of a triangle is given by:

`A=(bh)/(2)`

since base is 10 less than twice the height b=2h-10

plugin in those values and knowing area is 150

`150=`
`(h(2h-10))/(2)`

then solve for h

`300=2h^2-10h` this is quadratic equation

`h^2-5h-150=0`
factorizing (notice you can also use quadratic equation)

`(h-15)(h+10)=0`
which positive solution (height cant be negative) is h=15
then the base is b=2(15)-10=20