Someone -!
the lengths of the sides of an isoceles trapezoid are 10,10,13, and 19. compute the length of one diagonal of the isoceles trapezoid. express your answer in simplified radical form.

d = √347

Step-by-step explanation:

You can use Pythagoras' theorem twice to determine the length of the diagonal.

Consider the isosceles trapezoid PQRS in the diagram below.

ST = ½(19 - 13) = ½ × 6 = 3

∆PST is a right triangle

∴ PT² + 3² = 10²

  PT² = 10² - 3² = 100 - 9 = 91

∆PRT is a right triangle.

∴ PR² = RT² + PT²

  PR² = 16²  +  91 = 256 + 91 = 347

  PR = √347

The length of the diagonal is √347

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

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