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quadratic word problems

Algebra
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width of triangle is 4ft less than the length. The area is 10ft^2. Find the length and width

Jul 19th, 2014

Let's start with triangle area. The area of a triangle is 1/2 * base * height. In this problem it looks like they use width instead of height but you still have to multiply the two numbers. In order to successfully use the formula, the base and height measurements must have a right angle between them. The problem does not state what type of triangle it is but as long as the width and length lines make a right angle, you can find the area of the triangle. 

We start with w + 4 = L  and Area = 1/2 * w * L. Substitute L for the prev. expression of W and you get:Area = 1/2 * w * (w + 4) = 1/2 * ( w^2 +4w) = 1/2w^2 + 2w = Area. = 10 ft^2. Now subtract 10 from both sides and you get the quadratic  1/2w^2 + 2w - 10 = 0.  Now we can solve for w using the quadratic equation:

(-b +/- squareroot( b^2 - 4*a*c) ) / (2*a)  and so plugging in 1/2 for a, 2 for b, and -10 for c. We thus get:

(-2 +/- squareroot( 2^2 - 4 * 1/2 * -10) ) / (2 * 1/2) , and after evaluating this we get two roots, 2.899 and -6.899. These are the roots for your final answer. If you need more from this problem please contact me .

Jul 20th, 2014

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Jul 19th, 2014
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Jul 19th, 2014
Dec 7th, 2016
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