The area of an isosceles trapezoid is 72m2 and its diagonals are perpendicular. find the length of a diagonal.

12 meters.

Step-by-step explanation:

Let h represent the length of each diagonal of the given isosceles trapezoid.

We have been given that the area of an isosceles trapezoid is and its diagonals are perpendicular.

We know that area of a trapezoid with perpendicular diagonals is equal to half the product of diagonals., where,

represents diagonals of trapezoid.

Since both diagonals of isosceles trapezoid are congruent, so our formula would be:

Upon taking square root of both sides of our equation we will get,

Therefore, the length of each diagonal of our given trapezoid is 12 meters.

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step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15