+1622 We can use similar triangles here. First of all, ABC is an isosceles triangle because the altitude bisects the base, and thus forms two congruent triangles on each side by SAS congruency...
Angle BAD = angle FCB because both angles = 180 - 90 - angle B through angle-chasing. Ang le BAD = angle DAC, so we now can form a general similarity statement:
Triangle HCD ~ Triangle CAD. This means that AD / CD = CD / HD.
Let CD = s: \({16\over{s}} = {s\over{5}} \), and then cross multiplying yields \(80 = s^2\), square rooting both sides gives \(s = 4\sqrt{5}\).
Because the area of ABC = bh/2 = AD * BC/2 = AD*DC, we can substitute = 16 * 4sqrt(5) = 64sqrt(5), our final answer.
+1622 We can use similar triangles here. First of all, ABC is an isosceles triangle because the altitude bisects the base, and thus forms two congruent triangles on each side by SAS congruency...
Angle BAD = angle FCB because both angles = 180 - 90 - angle B through angle-chasing. Ang le BAD = angle DAC, so we now can form a general similarity statement:
Triangle HCD ~ Triangle CAD. This means that AD / CD = CD / HD.
Let CD = s: \({16\over{s}} = {s\over{5}} \), and then cross multiplying yields \(80 = s^2\), square rooting both sides gives \(s = 4\sqrt{5}\).
Because the area of ABC = bh/2 = AD * BC/2 = AD*DC, we can substitute = 16 * 4sqrt(5) = 64sqrt(5), our final answer.
