The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base? Question 2 options: 7 m 8 m 14 m 15 m

H=6+b

a = (1/2) bh

a=56

56 = (1/2) bh

times 2 both sides

112=bh

h=6+b

112=b (6+b)

112=b²+6b

minus 112 both sides

0=b²+6b-112

factor

what 2 numbers multily to get - 112 and add to get 6

-8 and 14

0 = (b-8) (b+14)

set to zero

b-8=0

b=8

b+14=0

b=-14

false, measures can't be negative

base=8

h=6+b

h=6+8

h=14

height=14

base=8

Triangle Area = (1/2) (base * height)

56 = (1/2) (base * (base + m))

112 = base^2 + base*m

base^2 + base*m - 112 = 0

By trial and error, we can try base = 1, height = 7, etc

base = 8

height = 14