A triangle has an area of 10cm^2. The height of the triangle is 4cm longer than three times the base. (((((((Find the height and base of the triangle)))))))

Question

A triangle has an area of 10cm^2.  The height of the triangle is 4cm longer than three times the base.             (((((((Find the height and base of the triangle)))))))

anonymous · Answer

Area of a triangle= 1/2 base x height
10= 1/2 (b)(3b+4)

anonymous · Answer

solve that out for b to get your base 
and then the height is 3b+4

anonymous · Answer

.5base x height???

anonymous · Answer

do I want to move everything over to the left except the base?

anonymous · Answer

isolate the b on one side, so yes

anonymous · Answer

10= 1/2 (b)(3b+4)
10= 1/2 (3b^2+4b)
20= 3b^2+4b
3b^2+4b-20= 0

anonymous · Answer

(3b+10)(b-2)= 0
3b=-10 or b=2
b=-10/3

anonymous · Answer

However, if you think about it logically, can a base ever be negative?

anonymous · Answer

No it can not

anonymous · Answer

Thus, the base is 2 and the height is 
3(2)+4= 6+4=10

anonymous · Answer

understand?

anonymous · Answer

the height is 10??

anonymous · Answer

yes, because the height= 3b+4
and the base is 2
so
3(2)+4
6+4
10

anonymous · Answer

0r$$-\frac{ 10 }{ 3 }$$

anonymous · Answer

A base or height can never be negative though

anonymous · Answer

ok I got it.

anonymous · Answer

okay cool :)