The height of a triangle is 6 in. less than the length of the base. The area of the triangle is 80 in. squared. What is the height and base of the triangle?

Answer 1

The height, H, is 6 inches less than the base, B

Mathematically, H = B - 6

Or, H + 6 = B

The area (A) is (B/2) x H

So using the relationship between the base and the heightwe can substitute (H + 6) for Bto get:

((H + 6)/2) x H = Area = 80

Distribute H over the binomial, (H + 6) and the equation becomes:

(H² + 6H)/2 = 80; Now multiply both sides by 2 to remove the denominator:

H² + 6H = 160, then rearrange to put the equation into a standard quadratic form: To do this subtract 160 from both sides:

H² + 6H -160 = 0

Now use the quadratic formula to solve for H. x = (-b +/1 √b2 - 4ac)/2a. For this equation, a = 1, b = 6, and c = -160, so plug those in and:

b² = 36

4ac = 4 x (-160) = -640

b2 - 4ac = 36 - (-640) = 676√

√676 = 26, so

x =( -6 = +/- 26)/2

x = (-6 + 26)/2 = 20/2 = 10, or

x = (-6 - 26))/2 = -32/2 = -16

But the length cannot be negative, so x must be the positive root, 10.

So the height is 10 inches, and the base is 16 inches.

If this is correct then using those for B/2 x H = A must be correct.

Let's check:

B = 16

H = 10

B/2 = 16/2 = 8

8H = 8 x 10 = 80. Check.

Hope this helps

Answer 2

The formula for the area of a triangle is .5*base*height.

So, they give us height=base-6

Now we just plug everything in!

80=.5*base*height

Now we have two variables in that equation, so we need to use the (height = base-6) to get rid of one of the variables. Now we have 80=.5*(base)*(base-6).

We can move the .5 to the other side to get 160=base*(base-6). Now we need to distribute base into the parethesis to get the following.

160=base^2-6*base.

Now recognize that this is in the form of a quadratic (ax^2+bx+c=0), so we need to arrange it like so.

base^2-6*base-160=0

Now use the quadratic formula (x=(-b+-sqrt(b^2-4ac))/(2a))

Plugging in our formula gives us...... base=(6+-sqrt(6^2-4(1)(-160))/(2*1)

So, solving this gives us base =16 and base =-10.

Does a negative length make sense? No, so our length for base is 16.

Now we need to find the height. Recall our formula from earlier that says height=base-6.

So, height=16-6=10.

So if height=10 and base=16, does that give us an area of 80? Let's check. area=.5*16*10=80.

Yes, it works. So height =10in and base=16in

Answer 3

You have to create an equation.

They give you the area so you have to connect that to what you are looking for.

To find the area of a triangle you need the base and height.

(b*h) / 2 = Area

Then start plugging the information in:

area = 80

base = b (unknown, so lets make it "b")

height = b - 6 (because height is 6 inches less then the base)

Solve for "b"

Now go back to the triangle area formula and plug in the values you have and solve for the height:

area = 80

base = whatever you found it to be

height = h