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?

2 Answers
Mar 10, 2018

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

Mar 10, 2018

Answer:

#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 #