The area of a triangular sheet of paper is 69 square inches. One side of the triangle is 5 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.

Question

dtan5457 · Answer

woops give me a sec i made a mistake

dtan5457 · Answer

let the altitude be x and the 
height be 3x+5 

69=(3x+5)(x)(1/2)

138=3x^2+5x

3x^2+5x-138=0 

solve that trinomial

dtan5457 · Answer

do you know how to use the quadratic formula? @Ehoyle26

dtan5457 · Answer

gonna need a response for further help :)

anonymous · Answer

no, I'm barely getting back into math again after almost 10 years

dtan5457 · Answer

quadratic formula=
$$\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a}$$

dtan5457 · Answer

a=3
b=5
c=-138

in your case

dtan5457 · Answer

$$\frac{ -5\pm \sqrt{25+1656} }{ 6 }$$

dtan5457 · Answer

solve that

anonymous · Answer

So x= -23/3 and x=6

dtan5457 · Answer

you will discard the negative part as it's not possible to have a negative length of a triangle

dtan5457 · Answer

x=6

let the altitude be x 
and the height be 3x+5 

plug x=6 back into to get altitude and height

anonymous · Answer

so, the altitude is 6 and the height is 23?

dtan5457 · Answer

Yes

anonymous · Answer

Thank you so much! I appreciate your help!