The height of a triangle is 5 units more than twice it's base. If the area of a triangles is 21 square units, what is its height?

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Answer 1 · 2018-04-19T12:56:17

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We know that Area of a triangle is given by #A=(bh)/2#

where #h=2b+5# and #A=21#. Then

#21=b(2b+5)/2#

#42=2b^2+5b# Then #2b^2+5b-42=0#

#b=(-5+-sqrt(25+4·42·2))/4=(-5+-19)/4#

There are two possible values for b #b=7/2# and #b=-6# rejected

With this value, substitution in #h=2b+5=2·7/2+5=12#

And both dimensions are now calculated.

#A=(7/2·12)/2=42/2=21#