Chapter 9.4, Problem 11PSB

a.

To determine

To calculate: The length of ABhere AC and BCare xand y

Answer to Problem 11PSB

The length of AB is $\sqrt{x^2+y^2}$

Explanation of Solution

Given: Lengths of AC and BCare as follows:

AC = x

BC = y

Concept used: Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Calculation: Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

  ${\left(AB\right)}^2={\left(AC\right)}^2+{\left(BC\right)}^2$

  ${\left(AB\right)}^2=x^2+y^2$

  $AB=\sqrt{x^2+y^2}$

Conclusion: Hence, the length of AB is $\sqrt{x^2+y^2}$

b.

To determine

To calculate: The length of AB here AC and BC are $2$ and x

Answer to Problem 11PSB

The length of AB is $\sqrt{4+x^2}$

Explanation of Solution

Given: Lengths of AC and BC are as follows:

AC = $2$

BC = x

Concept used: Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

Calculation: Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

  ${\left(AB\right)}^2={\left(AC\right)}^2+{\left(BC\right)}^2$

  ${\left(AB\right)}^2={\left(2\right)}^2+x^2$

  $AB=\sqrt{4+x^2}$

Conclusion: Hence, the length of AB is $\sqrt{4+x^2}$

c.

To determine

To calculate: Thelength of ABhere the lengths of AC and BC are $3a$ and $4a$

Answer to Problem 11PSB

The length of AB is $5a$

Explanation of Solution

Given:Length of AC and BC are as follows:

AC = $3a$

BC = $4a$

Concept used: Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

Calculation: Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

  ${\left(AB\right)}^2={\left(AC\right)}^2+{\left(BC\right)}^2$

  ${\left(AB\right)}^2={(3a)}^2+{\left(4a\right)}^2$

  $AB=a\sqrt{9+16}$

  $AB=5a$

Conclusion: Hence, the length of AB is $5a$

d.

To determine

To calculate: Thelength of BC

Answer to Problem 11PSB

The length of BC is $12$ c

Explanation of Solution

Given: Lengths of AB and AC are as follows:

AB = $13c$

AC = $5c$

Concept used: Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

Calculation: Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

  ${\left(AB\right)}^2={\left(AC\right)}^2+{\left(BC\right)}^2$

  $169c^2=25c^2+B{C}^2$

  $BC=12c$

Conclusion: Hence, the length of BC is $12$ c