Question

The height of a triangle is 4 inches. Greater than twice it's base. The area of the triangle is no more than 168 in.². Which any quality can be used to find the possible lengths, x, of the base of the triangle

Answer 1

Explanation:

this problem seeks to test our knowledge on word problems and algebra

Solution

let the base be x, and

the height h = 2x+4

We know that area of a triangle is given as

`A= (1)/(2) b*h`

substituting our given values we have

`168= (1)/(2) x*(2x+4)\\\\168= (2x^2+4x)/(2) \\\\168= x^2+2x\\\\`

re-arranging we have

`x^2+2x-168=0\\\\`

we can now find two factors that will add up to give 2 and multiply to give -168

they are 14 and -12

`x^2-14x+12x-168=0\\\\x(x-14)+12(x- 14)=0\\\\x+12=0\\\\x=-12\\\\x-14=0\\\\x=14`

The possible base of the triangle is 14 in

and the height is

`h= 2x+4\\\\h=2(14)+4\\\\h= 28+4\\\\\h= 32 in`