Recall that A = 1/2bh.
We are given that h = 4+2b
So, putting it all together:
168 = 1/2 b(4+2b)
168 = 1/2(4b + 2b^2)
168 = 2b + b^2
b^2 + 2b - 168 = 0.
Something that multiplies to -168 and adds to 2? There's a trick to this.
Notice 13^2 = 169. So, it's more than likely in the middle of the two numbers we're trying to find. So let's try 12 and 14. Yep. 12 x 14 = 168. So this factors into (b+14)(b-12) So b = -14 or b =12. Is it possible to have a negative length on a base? No. So 12 must be our answer.
Let's check this. If 12 is our base, then according to our problem, 2*12 + 4 would be our height... or 28. so what is 12 * 28 /2?
196. Check.
Hope this helped!
1) we change the inequality sign of inequality by equality sign. x²+2x-168=0 x=[-2⁺₋√(4+672)] / 2 x=(-2⁺₋√676)/2 we have two solutions: x₁=(-2-√676)/2=-14 x₂=(-2⁺√676)/2=12
2) we make intervals with these values. (-∞, -14<span> ) </span><span>(-14,12) </span>(12, +∞)
3) we check it out if these intervals work (-∞,-14), For instead; if x=-15⇒ (-15)²+2(-15)-168=27>0. this solution interval don´t work.
(-14,12), For example; if x=1 ⇒(-1)²+2(1)-168=-168<0 this solution interval works. but the solutions have to be always positive numbers, therefore, the solution is: (0,12).
(12,+∞) , For example, if x=13 ⇒ (13)²+2(13)-168=27>0, this solution interval don´t work.
Answer: the inequality is : <span>x(2x+4)/2<168, and the interval solution is (0,12) for the values of the base. </span>
