Solve four square root of six plus eight square root of four and explain whether the answer is rational or irrational.

the answer twelve square root of ten is rational because the sum of a rational number and irrational number is a rational number.

the answer four square root of six plus sixteen is irrational because the sum of a rational number and irrational number is an irrational number.

the answer twelve square root of ten is irrational because the sum of a rational number and irrational number is an irrational number. the answer four square root of six plus sixteen is rational because the sum of a rational number and irrational number is a rational number.

The answer twelve square root of ten is rational because the sum of a rational number and irrational number is a rational number.

23

step-by-step explanation:

(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