Question

Hi! I've honestly been trying to work out this problem for quite a while so far but I'm honestly really stuck on it ugh. Could someone possibly help me out! Thanks!
The height of a triangle is four more than twice the length of the base. If the area of the triangle is 80 in.squared, find the length of the base and the height. (HINT: Formula for the area of a triangle is A=1/2 bh )

Answer 1

Alright,So we know that the area is 80 in and the height is 2x+4 because it is 4 more than twice the length.

Answer 2

To find the area of a triangle you do
\[base*width*\frac{ 1 }{ 2 }\]
Just set that equal to 80 and solve for x.

Answer 3

Short answer: b=8, h=10

So...

Hight is 2 times base plus 4.
h=2b+4
If 1/2b*h = 80,

that means b*h = 160.

So if we know h=2b+4, and b*h = 160, we can determine...

b*(2b+4) = 160.
2b^2 + 4b = 160
b^2 + 2b = 80
b^2 = 80-2b

Notice that 8 squared = 64
2*8 = 16,

64+18 = 80, so 8 works for this answer.

That means b=8. From there we can determine that height is 10, because b*h=160.

b=8, h=10

Good luck!