Question 1187911
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The area of a triangle is found by dividing the product of the altitude and the base by 2, to wit:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \frac{ab}{2}]


Since you know that the altitude is 2 cm longer than twice the base, you can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ 2b\ +\ 2]


Then since you are given that the area is 42 cm², you can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 42\ =\ \frac{(2b\,+\,2)b}{2}]


Simplifying:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b^2\ +\ b\ -\ 42\ =\ 0]


Solve the factorable quadratic for the positive root (a negative number for the measure of the base of a triangle would be absurd).  Then calculate the altitude from *[tex \Large a\ =\ 2b\ +\ 2]

																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

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