The height of a triangle is 4 inches more than twice the length of the base. The area of the triangle is 35 square inches. What is the height of the triangle?

2 Answers
Feb 24, 2016

#14#

Explanation:

Let the Base of the #triangle# be #color(red)(x#

Then the Height will be #color(red)(2x+4#

Area of #triangle#=#color(brown)(1/2bh#

Where,

#color(brown)(b=base,h=height,Area=35# (in this case)

Substitute the values into the equation

#rarr35=1/2(2x+4)(x)#

#rarr35=((cancel2x+cancel4))/cancel2(x)#

#rarr35=(x+2)(x)#

#rarr35=x^2+2x#

Subtract #35# both sides

#rarr0=x^2+2x-35#

Rewrite the equation in the Standard form

#x^2+2x-35=0#

Factor the equation

#rarr(x+7)(x-5)=0#

So we have #color(blue)(x=-7,5#

length or distance should not be #uln##uleulgulaultuliulvule# numbers

So #color(orange)(x=5#

They have asked us to find the Height

So,

#rArrcolor(green)(Height=2x+4=2(5)+4=10+4=14#

Feb 24, 2016

height #= 14# inches.

Explanation:

Let the height be #h# and the base be #h# (inches)
#h=2b+4#

Area: #(bh)/2=35#

#color(white)("XXX")bxx(2b+4)=70#

#color(white)("XXX")2b^2+4b=70#

#color(white)("XXX")b^2+2b-35=0#

#color(white)("XXX")(b-5)(b+7)=0#

#rArr b=5 or b=-7#

Since the base must be positive:
#color(white)("XXX")b=5#
and
#color(white)("XXX")h=2b+4=14#