Question

(03.06 MC) triangle ABC with segment BD where point D is between points C and A, BC equals x, BD equals y, CD equals w, DA equals z, and BA equals v What expression represents the value of y? y equals the square root of quantity x times v end quantity y equals the square root of quantity w times z end quantity y equals the square root of quantity w times the sum of w plus z end quantity y equals the square root of quantity z times the sum of w plus z end quantity

Answer 1

Answer:

The answer is y equals the square root of quantity w times z

Step-by-step explanation:

This is the only answer that actually makes sense to me.  First I used distance formula and then figured out I was wrong... I am actually taking this test right now.

Answer 2

The triangle represents a right-angled triangle.

The equation that represents the value of y is: $\mathbf{y = \sqrt{x^2 - w^2} }$

Considering triangle BCD, we have:

$\mathbf{BC^2 = CD^2 + BD^2}$ --- Pythagoras theorem

Substitute values for BC, CD and BD

$\mathbf{x^2 = w^2 + y^2}$

Subtract w^2 from both sides

$\mathbf{x^2 - w^2 = y^2}$

Take square roots of both sides

$\mathbf{\sqrt{x^2 - w^2} = y}$

Rewrite as:

$\mathbf{y = \sqrt{x^2 - w^2} }$

Hence, the equation that represents the value of y is: $\mathbf{y = \sqrt{x^2 - w^2} }$

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