# math

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The base of a triangle is 10 cm longer than the height. Determine the height of the triangle if its area is 48 cm^2.

-I just plugged in number and got 6cm for the height and 16cm for the base. But I need to show work and I cant remember how to solve this.

• math -

The height h is b - 10

(1/2) b (b-10) = 48
b^2 -10b = 96
(b-16)*(b+6) = 0
b = 16. h = b-10 = 6
The other root (b = -6) makes no sense.

• math -

The triangle area is A = bh/2 where b = the base and h = the height.

Therefore, A = (h + 6)h/2 = 24. I imagine you can take it from here.

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