Chapter 9.3, Problem 2PSA

a

To determine

To find:The value of $2x$

Answer to Problem 2PSA

The value of $2x=8\sqrt{5}$

Explanation of Solution

Given information:The following equations can be generated by applying Pythagoras in different triangles

  $81=z^2+y^2$

  $z^2=x^2+25$

  $y^2=x^2+16$

Formula used:Linear equations have been solved

Calculation:Hence, on substituting the values of y and z from the last two equations into the first one, we get

  $x=4\sqrt{5}$

Thus, we get

  $2x=8\sqrt{5}$

b

To determine

To find:The value of $\frac{y}{2}$

Answer to Problem 2PSA

The value of $\frac{y}{2}=3$

Explanation of Solution

Given information:The following equations can be generated by applying Pythagoras in different triangles

  $81=z^2+y^2$

  $z^2=x^2+25$

  $y^2=x^2+16$

Formula used:Linear equations have been solved

Calculation:Hence, on substituting the values of x and z from the equations one and three into the second one, we get

  $y=6$

Thus, we can say that

  $\frac{y}{2}=3$

c

To determine

To find:The value of $z+8$

Answer to Problem 2PSA

The value of $z+8=8+3\sqrt{5}$

Explanation of Solution

Given information:The following equations can be generated by applying Pythagoras in different triangles

  $81=z^2+y^2$

  $z^2=x^2+25$

  $y^2=x^2+16$

Formula used:Linear equations have been solved

Calculation:Hence, on substituting the values of x and y from the equations one and two into the third one, we get

  $z=3\sqrt{5}$

Thus, we get

  $z+8=8+3\sqrt{5}$