Question 694541
The altitude of a triangle is 2 metres longer than its base what are the dimensions of the altitude and the base if the area of the triangle is 40 metres squared.


Formula for area of a right-triangle: {{{A = (1/2)BH}}}, where A is the area of the triangle, H is the height (altitude) and B, the base


Since H (altitude) is 2 metres longer than B (base), then it can be said that B = H - 2. As A or area = 40 {{{A = (1/2)BH}}} becomes: {{{40 = (1/2)(H - 2)H}}}


{{{40 = (1/2)(H^2 - 2H)}}} ----- {{{40 = (H^2 - 2H)/2}}} 


{{{H^2 - 2H = 80}}} ---- Cross-multiplying


{{{H^2 - 2H - 80 = 0}}}


(H + 8)(H - 10) = 0


H = - 8 (ignore as ray/segment/line CANNOT be negative)


H, or height = {{{highlight_green(10)}}} metres


Base = 10 - 2, or {{{highlight_green(8)}}} metres


You can do the check!!


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