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Type: Open-Ended
Category: Triangles
Level: Grade 11
Author: nsharp1
Created: 4 years ago

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Triangles Question

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For

$Delta ABC$ , as seen below, let the intersection of the altitude from vertex

$B$ and side

$bar{AC}$ be point

$D$ (not labeled). Also, let

$b = AC, \ c=AB, \ a = BC, \ x = AD, \ y=CD$ , and

$h = BD$ . Finally, let

$P = a+b+c$ and

$s=P/2$ .

The area of this triangle can be expressed using Heron's formula,

$A_{Delta ABC} = sqrt(s(s-a)(s-b)(s-c))$ , where

$s = (a+b+c)/2$ . The following questions will derive this formula.

Acute Triangle Height v2

Grade 11 Triangles

The final form of the equation from the previous step should look like

$h^2 = (4b^2c^2 - (a^2 - b^2 - c^2)^2)/(4b^2)$ . Using difference of squares and perfect square trinomial formulas, simplify the numerator of this equation. Hint: the difference of squares formula will need to be applied more than once.