khekking
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# 2. The height of a triangle is 5 m less than its base. The area of the triangle is 42 m2. Find the length of the base. (Points : 1)

Let's start with what we know Area: $42 = \frac{1}{2}bh$ where 42 is the area, b = base, and h = height Height: Since we know the height is 5 less than the base, we can write that as an equation. $h = b - 5$ Now let's go and plug $h = b - 5$ into $42 = \frac{1}{2}bh$ $42 = \frac{b}{2}(b-5)$ Let's distribute b over (b-5) $42 = \frac{ b^{2} - 5b }{2}$ Let's move 42 over to the right side to make a quadratic formula $0 = \frac{1}{2} b^{2} - \frac{5}{2}b - 42$ Let's plug that into the quadratic equation, which is: $\frac{-b +/- \sqrt{ b^{2} - 4ac } }{2a}$ And we can now plug the pieces in to calculate b $\frac{- (-\frac{5}{2}) +/- \sqrt{ (-\frac{5}{2})^{2} - 4 (\frac{1}{2})(-42) } }{2 (\frac{1}{2}) }$ $\frac{\frac{5}{2} +/- \sqrt{ \frac{25}{4} +84 } }{1 }$ ${\frac{5}{2} +/- \sqrt{ \frac{361}{4} } }$ ${\frac{5}{2} +/- { \frac{19}{2} }$ Since we can't have a negative value for b (a base can't be negative meters), let's add: ${\frac{5}{2} + { \frac{19}{2} }$ ${ \frac{24}{2} }$ $12 = b$ So the base of the triangle is 12m