Question

The area of a triangle is 24cm² [squared]. The base is 8cm longer than the height. Use this information to set up a quadratic equation. Solve the equation to find the length of the base?

Answer 1

Let the length of the base is `x`,so height will be `x-8`

so,area of the triangle is `1/2 x (x-8)=24`

or, `x^2 -8x-48=0`

or, `x^2 -12x +4x-48=0`

or, `x(x-12) +4(x-12)=0`

or, `(x-12)(x+4)=0`

so,either `x=12` or `x=-4` but length of triangle can't be negative,so here length of the base is `12` cm

Answer 2

`12 cm`

Explanation:

The area of a triangle is `("base " xx " height" )/2`

Let the height be `x` then if the base is 8 longer, then the base is `x+8`

`=> (x xx (x+8) )/2 = " area "`

`=> (x(x+8))/2 = 24`

`=> x(x+8) = 48`

Expanding and simplifying...

`=> x^2 + 8x = 48`

`=> x^2 +8x - 48 = 0`

`=> (x-4)(x+12) = 0`

`=> x = 4 " and " x = -12`

We know `x = -12` can't be a solution as length can't be negative

Hence `x = 4`

We know the base is `x+8`

`=> 4+8 = 12`