Answer:
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 [tex]72\text{ m}^2[/tex] and its diagonals are perpendicular.
We know that area of a trapezoid with perpendicular diagonals is equal to half the product of diagonals.[tex]\text{Area of trapezoid}=\frac{h_1\times h_2}{2}[/tex], where,
[tex]h_1\text{ and } h_2[/tex] represents diagonals of trapezoid.
Since both diagonals of isosceles trapezoid are congruent, so our formula would be:
[tex]\text{Area of trapezoid}=\frac{h\times h}{2}[/tex]
[tex]72\text{ m}^2=\frac{h^2}{2}[/tex]
[tex]2*72\text{ m}^2=\frac{h^2}{2}*2[/tex]
[tex]144\text{ m}^2=h^2[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]\sqrt{144\text{ m}^2}=h[/tex]
[tex]12\text{ m}=h[/tex]
Therefore, the length of each diagonal of our given trapezoid is 12 meters.
