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What is the height of a trapezoid whose height is the same length as its smaller base with the other base being 2 cm greater and has an area of 42 sq cm?
Wiki User
∙ 13y ago
Let the bases be x+2, x and the height be x because it's the same size as the smaller base:
1/2*(sum of parallel bases)*height = area
1/2*(x+2+x)*x = 42 sq cm
Multiply both sides by 2:
(x+2+x)*x = 84
Multiply out the brackets:
x2+2x+x2 = 84
2x2+2x-84 = 0
Solving the above quadratic equation works out as:
x = -7 or x = 6 it must be the latter because dimensions can't be negative.
Therefore: height = 6 cm
Check: 1/2*(8+6)*6 = 42 sq cm
Wiki User
∙ 13y ago
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