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The base of a triangle is 4 feet shorter than its altitude, and the area of the triangle is 126 square feet. Find the base and the altitude.

Solution:

Let $$b$$ be the base and $$a$$ be the altitude of the triangle.

$$b = a- 4$$

$$A_t = 126$$

$$A_t = \frac{1}{2}ba$$

$$126 = \frac{1}{2}ba$$

$$a = \frac{252}{b}$$

$$b = \frac{252}{b} -4$$

$$b^2 = 252 - 4b$$

$$b^2+4b- 252=0$$

$$(b-14)(b+18) = 0$$

$$b = 14$$

$$a = 14+4 = 18$$

Thus, the base of the triangle is 14 feet and the altitude is 18 feet