Posted by **Kim** on Wednesday, January 14, 2009 at 11:33am.

The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base.

- Algebra -
**DrBob222**, Wednesday, January 14, 2009 at 12:33pm
Area of triangle = 1/2(height x base)

The problem states that base is 8 cm greater than the height; therefore, base-8 = height.

A = 1/2(b*h)

42 = 1/2(b*[b-8])

84=(b^2-8b)

rearrange to

b^2 - 8b -84

factor to

(b+8)(b-14)

Therefore, b = -8 cm which makes no sense and

b = +14 cm

and height = 14-8 = 6

Check:

1/2(b*h) = area

1/2(14*6) = 1/2(84)=42

Check my work.

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