The base of a triangle is twelve more than twice its height. If the area of triangle is 53 square centimeters, what is its base and height?

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Answer 1 · 2015-12-10T02:15:36

#h~~4.874# #"cm",b~~21.748# #"cm"#

#A_"triangle"=1/2bh#

"The #color(green)("base")# of a triangle is #color(red)("twelve more")# than #color(blue)("twice its height")#."

From this we can say that:

#color(green)b=color(blue)(2h)+color(red)12#

So, if #A=1/2bh#, we can replace #b# with #2h+12#.

#A=1/2(2h+12)h#

#53=1/2(2h+12)h#

#53=(h+6)h#

#53=h^2+6h#

#h^2+6h-53=0#

Use the quadratic formula.

#h=(-6+-sqrt(6^2-4(-53)(1)))/2#

#h~~4.874#

(Ignore the negative answer—height can't be negative.)

#b~~2(4.874)+12#

#b~~21.748#