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A triangle has a base length (x-8) cm and a height of 2x cm. If its area is 20cm^2 , calculate its height and base length.

Sagot :

reinhard10158

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

20 = (x-8)×2x/2

40 = (x-8)×2x

20 = (x - 8) × x = x² - 8x

x² - 8x - 20 = 0

the solution to such a square equation is defined

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 1

b = -8

c = -20

x = (8 ± sqrt(64 - 4×-20))/2 = (8 ± sqrt(64+80))/2 =

= (8 ± sqrt(144))/2 = (8 ± 12)/2 = 4 ± 6

x1 = 4 + 6 = 10

x2 = 4 - 6 = -2

but a negative x would also create a negative base length and negative height, so this is not valid for our problem.

that leaves us with x = 10

a base length of x-8 = 10-8 = 2 cm

and a height of 2x = 2×10 = 20 cm

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