Question

the base of a triangle is five less than twice it’s height, if the area of the triangle is 6 cm^2, find the length of the base

Answer 1

Answer:

Base = 3 cm

Step-by-step explanation:

Area of a triangle =  $\frac{1}{2} bh$

Let h = height

base =  2 times the height - 5; b = 2h-5

Area = 6 cm²

 A = $\frac{1}{2}bh$

$6 =\frac{1}{2}(2h - 5)(h)$             Multiply 2h(h) -5(h)

$6 (2) = 2(\frac{1}{2})(2h^{2} - 5h$      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