Let $Δ X Y Z$ be right angle triangle with right angle at Z. Let $A_{X}$ denotes the area of the circle with diameter YZ. Let $A_{Y}$ denote the area of the circle with diameter XZ and let $A_{Z}$ denotes the area of the circle diameter XY. Which of the following relations is true?

A_{Z} = A_{X} + A_{Y}

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A_{Z} = A_{X}^{2} + A_{Y}^{2}

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A_{Z}^{2} = A_{X}^{2} + A_{Y}^{2}

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A_{Z}^{2} = A_{X}^{2} - A_{Y}^{2}

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Solution

The correct option is A $A_{Z} = A_{X} + A_{Y}$
In $△ X Y Z$ , using Pythagoras theorem,
$X Y^{2} = X Z^{2} + Y Z^{2}$
$π X Y^{2} = π X Z^{2} + π Y Z^{2}$ (Multiply by $π$ )
$A_{z} = A_{x} + A_{y}$

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Let ΔXYZ be right angle triangle with right angle at Z. Let AX denotes the area of the circle with diameter YZ. Let AY denote the area of the circle with diameter XZ and let AZ denotes the area of the circle diameter XY. Which of the following relations is true?

The correct option is A AZ=AX+AYIn △XYZ, using Pythagoras theorem,XY2=XZ2+YZ2πXY2=πXZ2+πYZ2 (Multiply by π)Az=Ax+Ay

Let $Δ X Y Z$ be right angle triangle with right angle at Z. Let $A_{X}$ denotes the area of the circle with diameter YZ. Let $A_{Y}$ denote the area of the circle with diameter XZ and let $A_{Z}$ denotes the area of the circle diameter XY. Which of the following relations is true?

The correct option is A $A_{Z} = A_{X} + A_{Y}$
In $△ X Y Z$ , using Pythagoras theorem,
$X Y^{2} = X Z^{2} + Y Z^{2}$
$π X Y^{2} = π X Z^{2} + π Y Z^{2}$ (Multiply by $π$ )
$A_{z} = A_{x} + A_{y}$