SOLUTION: The height of a triangle is 8 inches less than its base. The area of the triangle is 192 square inches. the height of the triangle is __ inches and the base of the triangle is __ i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The height of a triangle is 8 inches less than its base. The area of the triangle is 192 square inches. the height of the triangle is __ inches and the base of the triangle is __ i      Log On


   

Question 16701: The height of a triangle is 8 inches less than its base. The area of the triangle is 192 square inches. the height of the triangle is __ inches and the base of the triangle is __ inches.
Answer by bam878s(77) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the height any y = the base.
We know that x = y - 8 and 1%2F2+%2A+x+%2A+y= 192
Pluggin the x = y - 8 into the second equation yields
%281%2F2%29+%2A+%28y-8%29+%2A+y = 192
or
%281%2F2%29+%2A+y%5E2+-+4+%2A+y = 192
and
%281%2F2%29y%5E2+-+4y+-+192 = 0
then use the quadratic equation to solve for y
%284+%2B-+sqrt%28%28-4%29%5E2+-+4+%2A+%281%2F2%29+%2A+-192%29%29%2F%282+%2A+%281%2F2%29%29
y = 4 + 20 or y = 4 - 20. Since we are dealing with length then a negative value doesn't make sense so y = 4 + 20 = 24.
Now use y to solve for x.
x = y - 8 = 24 - 8 = 16.
So x = 16 = the height
and
y = 24 = the base
Check: 16 * 24 = 384
384 / 2 = 192