Question : In $\triangle$ABC, Z is a point on side BC, and AB = AC. If $\angle$AZB = 90° and BC = 42 cm, then what will be the length of BZ?
Option 1: 21 cm
Option 2: 32 cm
Option 3: 28 cm
Option 4: 35 cm
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Correct Answer: 21 cm
Solution :
In an isosceles triangle, if a line is drawn from the vertex of the equal sides to the base such that it is perpendicular to the base, it bisects the base. This line is also known as the altitude of the isosceles triangle.
Since AB = AC and $\angle$AZB = 90°, by the property of an isosceles triangle, the line AZ will bisect BC at Z. Therefore, BZ = CZ
So, if BC = 42 cm, then BZ = $\frac{BC}{2}$ = $\frac{42}{2}$ = 21 cm
Hence, the correct answer is 21 cm.
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