Chapter 9.6, Problem 9PSA

a.

To determine

To find:The missing side of the triangle where the other two sides are $16$ and $8\sqrt{5}$

Answer to Problem 9PSA

The missing side is $24$

Explanation of Solution

Given:

Two sides are $16$ and $8\sqrt{5}$

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

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

Let the missing side be x

  ${\left(x\right)}^2={\left(16\right)}^2+{\left(8\sqrt{5}\right)}^2$

Now, by dividing each side by 8 we get

  $x^2={\left(2\right)}^2+{\left(\sqrt{5}\right)}^2$

  $x=\sqrt{4+5}$

  $x=3$

As, we divided both the sides by $8$ so now we need to multiply the result by $8$ to get the answer.

  →$3\times 8=24$

Conclusion: Hence, the missing side is $24$

b.

To determine

To find:The missing side of the triangle where the other two sides are $700$ and $200$

Answer to Problem 9PSA

The missing side is $300\sqrt{5}$

Explanation of Solution

Given:

Two sides are $700$ and $200$

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

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

  $x^2={\left(700\right)}^2-{\left(200\right)}^2$

Now, by dividing both the sides by $100$ we get

  $x^2={\left(7\right)}^2-{\left(2\right)}^2$

  $x=\sqrt{45}$

  $x=3\sqrt{5}$

As, we divided both the sides by $100$ so now we need to multiply the result by $100$ to get the answer.

  →$3\sqrt{5}\times 100=300\sqrt{5}$

Conclusion: Hence, the missing side is $300\sqrt{5}$