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?

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