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?

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Answer 1 · 2018-03-10T13:33:30

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 · 2018-03-10T13:35:35

$12 cm$

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 $x+8$

$=> 4+8 = 12$