To find AC we need to find EC. We do this by using the Pythagorean Theorem to find a side with one side 7 and the hypotenuse root 130:
[tex] {a}^{2} = {b}^{2} + {c}^{2} \\ {c}^{2} = {a}^{2} - {b}^{2} \\ c = \sqrt{ {a}^{2} - {b}^{2} } \\ c = \sqrt{ {( \sqrt{130} )}^{2} - {(7)}^{2} }[/tex]
[tex]c = \sqrt{130 - 49} \\ c = \sqrt{81} \\ c = 9[/tex]
First, we single out the variable we want (C). Then, we plug in the numbers. We find that length EC is 9 inches. Therefore, AC is 24 + 9 = 33 inches.
To find AD, we must use the Pythagorean Theorem. Since this shape is symmetrical, we know that EB = ED, so ED = 7 in. Now we just need to find the hypotenuse:
[tex]a = \sqrt{ {b}^{2} + {c}^{2} } \\ a = \sqrt{ {(7)}^{2} + {(24)}^{2} } \\ a = \sqrt{49 + 576} \\ a = \sqrt{625} = 25[/tex]
First, we plug in the legs of the triangle, and then simplify. Therefore, the length AD is 25 inches.
Since this shape is a kite, ED and EB are congruent. Therefore, ED is 7 inches.
