Question

If the area of a triangle is 45 square inches and the base is 9 inches more than the height. Find the height of the triangle. (A=1/2bh)

*Please show work, thank you!*

Answer 1

6 Inches would be your answer :)

Answer 2

This problem can be represented with the following equation:
(x*x+9)/2= 45
Where x equals height and x+9 equals base. First we will find x.
→x*x+9= 90
→x²+9x= 90
-We divide 9 by 2 and then square the number. Then we add that number to both sides to obtain a perfect square trinomial. 9/2= 4.5; 4.5²=20.25
→x²+9x+20.25= 90+20.25
→x²+9x+20.25= 110.25
→(x+4.5)²= 110.25
→x+4.5= 10.5
→x= 10.5-4.5
→x= 6
Since x represents the height, the height of the triangle is 6 inches.
ANSWER: 6 inches