Question

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?

Answer 1

`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`

Answer 2

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`