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?

$14$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,

$rArrcolor(green)(Height=2x+4=2(5)+4=10+4=14$height = 14 inches.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