Question

5.
(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 x? (2 points)
x equals the square root of quantity w times the sum of w plus z end quantity
x equals the square root of quantity z times the sum of w plus z end quantity
x equals the square root of quantity w times y end quantity
x equals the square root of quantity w times z end quantity

1. thuhuong
The triangle represents a right-angled triangle.
The equation that represents the value of y is y = √x² – w²
What is a right-angle triangle, exactly?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees.
Perpendicular and the triangle’s base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.
Considering triangle BCD, we have:
BC² = CD² + BD² — Pythagoras theorem
Substitute values for BC, CD and BD
x² = w² + y²
Subtract w^2 from both sides
y² = x² – w²
Take square roots of both sides
y = √x² – w²
Hence, the equation that represents the value of y is  y = √x² – w²