\sqrt{3x^{10}}
3x
10

​

5

Step-by-step explanation:

√

3

x

+

10

=

x

To remove the radical on the left side of the equation, square both sides of the equation.

√

3

x

+

10

2

=

x

2

Simplify each side of the equation.

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3

x

+

10

=

x

2

Solve for  

x

.

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x

=

5

,

−

2

Exclude the solutions that do not make  

x

=

√

3

x

+

10

true.

x

=

5

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

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step-by-step explanation: