Answer:
Base = 3 cm
Step-by-step explanation:
Area of a triangle = [tex]\frac{1}{2} bh[/tex]
Let h = height
base = 2 times the height - 5; b = 2h-5
Area = 6 cm²
A = [tex]\frac{1}{2}bh[/tex]
[tex]6 =\frac{1}{2}(2h - 5)(h)[/tex] Multiply 2h(h) -5(h)
[tex]6 (2) = 2(\frac{1}{2})(2h^{2} - 5h[/tex] Multiply both sides by 2 to remove the fraction
12 = 2h²- 5h
2h ² - 5h - 12 = 0 Set the equation = 0 and factor
(2h + 3)(h - 4) = 0
2h + 3 = 0 or h - 4 = 0
2h = -3 h = 4
h = -3/2 or h = 4 Answer can not be negative so h = 4cm
The base is 2(4) - 5; The base = 8 - 5; base = 3 cm
