Question 280570
Start with your variables...
A = area of a triangle = 1/2*base*height
h = height of the triangle
b = base of the triangle
b = h + 6  :: the base is 6 cm > height
A = 20 cm^2
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Substitute what we know...
20 cm^2 = 1/2*b*h
20 = 1/2(h+6)*h
multiply both sides by 2
40 = (h+6)*h = h^2 + 6h
subtract 40 from both sides
0 = h^2 + 6h - 40
so
h^2 + 6h - 40 = 0
factor
(h+10)(h-4) = 0
which means our solutions are
h = -10
h = 4
of course negative height is nonsense
which means h = 4 is the solution to test
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substituting what we know about the base
b = h+6 = 10
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checking the area
1/2*4*10  = 20?
2* 10 = 20
Yes.
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Answer:
The height of the triangle is 4 cm.
The base of the triangle is 10 cm.
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Done