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 v?

a. v equals the square root of quantity z times y end quantity
b. v equals the square root of quantity w times z end quantity
c. v equals the square root of quantity w times the sum of w plus z end quantity
d. v equals the square root of quantity z times the sum of w plus z end quantity

Answer 1

The right-angled triangular is represented by the triangle.

The following equation reflects the value of y:

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

In terms of triangle BCD, we have us the Pythagoras theorem:

$\to BC^2=CD^2+BD^2$

Values for BC, CD, and BD can be substituted.

$\to x^2=w^2+y^2$

Subtraction of $w^2$ from both sides

$\to x^2-w^2=y^2$  

Calculate the square roots of both sides.

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

Rephrase as:

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

As a result, the equation representing the value of y is: $y=\sqrt{x^2-w^2}$

Learn more about the right-angled triangle:

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