Chapter 9.6, Problem 5PSA

a.

To determine

To find:The missing side of the triangle where other two sides are $9$ and $15$

Answer to Problem 5PSA

The missing side is $12$

Explanation of Solution

Given:

Two sides are $9$ and $15$

Concept used:

Here, we are using Pythagoras theorem.

Calculation:

Here, the formula is

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

Let the missing side be x

  ${\left(x\right)}^2={\left(15\right)}^2-{\left(9\right)}^2$

  $x=\sqrt{225-81}$

  $x=\sqrt{144}$

  $x=12$

  $12$

Conclusion: Hence, the missing side is $12$

b.

To determine

To find:The missing side of the triangle where other two sides are $6$ and $8$

Answer to Problem 5PSA

The missing side is $2\sqrt{7}$

Explanation of Solution

Given:

Two sides are $6$ and $8$

Concept used:

Here, we are using Pythagoras theorem.

Calculation:

Here, the formula is

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

  $x^2={\left(8\right)}^2-{\left(6\right)}^2$

  $x^2=64-36$

  $x=\sqrt{28}$

  $x=2\sqrt{7}$

Conclusion: Hence, the missing side is $2\sqrt{7}$

c.

To determine

To find:The missing side of the triangle where other two sides are $24$ and $26$

Answer to Problem 5PSA

The missing side is $10$

Explanation of Solution

Given:

Two sides are $24$ and $26$

Concept used:

Here, we are using Pythagoras theorem.

Calculation:

Here, the formula is

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

  $x^2={\left(26\right)}^2-{\left(24\right)}^2$

  $x=\sqrt{676-576}$

  $x=\sqrt{100}$

  $x=10$

Conclusion: Hence, the missing side is $10$

d.

To determine

To find:The missing side of the triangle where other two sides are $1.3$ and $1.2$ .

Answer to Problem 5PSA

The missing side is $0.5$

Explanation of Solution

Given:

Two sides are $1.3$ and $1.2$

Concept used:

Here, we are using Pythagoras theorem.

Calculation:

Here, the formula is

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

  $x^2={\left(1.3\right)}^2-{\left(1.2\right)}^2$

  $x^2=1.69-1.44$

  $x=\sqrt{0.25}$

  $x=0.5$

Conclusion: Hence, the missing side is $0.5$

e.

To determine

To find:The missing side of the triangle where other two sides are $16$ and $30$ .

Answer to Problem 5PSA

The missing side is $34$

Explanation of Solution

Given:

Two sides are $16$ and $30$

Concept used:

Here, we are using Pythagoras theorem.

Calculation:

Here, the formula is

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

  $x^2={\left(30\right)}^2+{\left(16\right)}^2$

  $x^2=900+256$

  $x=\sqrt{1156}$

  $x=34$

Conclusion: Hence, the missing side is $34$

f.

To determine

To find:The missing side of the triangle where other two sides are $20$ and $15$ .

Answer to Problem 5PSA

The missing side is $5\sqrt{7}$

Explanation of Solution

Given:

Two sides are $20$ and $15$

Concept used:

Here, we are using Pythagoras theorem.

Calculation:

Here, the formula is

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

  $x^2={\left(20\right)}^2-{\left(15\right)}^2$

  $x^2=400-225$

  $x=\sqrt{175}$

  $x=5\sqrt{7}$

Conclusion: Hence, the missing side is $5\sqrt{7}$

g.

To determine

To find:The missing side of the triangle where other two sides are $75$ and $21$ .

Answer to Problem 5PSA

The missing side is $72$

Explanation of Solution

Given: Two sides are $75$ and $21$

Concept used: Here, we are using Pythagoras theorem.

Calculation: Here, the formula is

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

  $x^2={\left(75\right)}^2-{\left(21\right)}^2$

  $x^2=5625-441$

  $x=\sqrt{5184}$

  $x=72$

Conclusion: Hence, the missing side is $72$

h.

To determine

To find:The missing side of the triangle where other two sides are $51$ and $24$

Answer to Problem 5PSA

The missing side is $45$

Explanation of Solution

Given: Two sides are $51$ and $24$

Concept used: Here, we are using Pythagoras theorem.

Calculation: Here, the formula is

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

  $x^2={\left(51\right)}^2-{\left(24\right)}^2$

  $x^2=2601-576$

  $x=\sqrt{2025}$

  $x=45$

Conclusion: Hence, the missing side is $45$

h.

To determine

To find:The missing side of the triangle where other two sides are $5\sqrt{7}$ and $12\sqrt{7}$ .

Answer to Problem 5PSA

The missing side is $13\sqrt{7}$

Explanation of Solution

Given: Two sides are $5\sqrt{7}$ and $12\sqrt{7}$

Concept used: Here, we are using Pythagoras theorem.

Calculation: Here, the formula is

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

  $x^2={\left(12\sqrt{7}\right)}^2-{\left(5\sqrt{7}\right)}^2$

  $x^2=1008-175$

  $x=\sqrt{833}$

  $x=13\sqrt{7}$

Conclusion: Hence, the missing side is $13\sqrt{7}$