Question 916880

The base of a triangle is 14 inches more than 4 times the height. If the area is 60 square inches, find the base and the height
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Let height be H
Then base-length = 4H + 14
Since area = 60, then we can say that: {{{(1/2)H(4H + 14) = 60}}}
{{{(H(4H + 14))/2 = 60}}}
{{{4H^2 + 14H = 120}}}} ----- Cross-multiplying
{{{4H^2 + 14H - 120 = 0}}}
{{{2(2H^2 + 7H - 60) = 2(0)}}}  
{{{2H^2 + 7H - 60 = 0}}}
(H - 4)(2H + 15) = 0
H, or height = {{{highlight_green(4)}}} inches               OR              {{{H = - 15/2}}} (ignore)
Base-length: 4(4) + 14, or 16 + 14, or {{{highlight_green(30)}}} inches