abcd is a kite, so \\( \\overline { a c } \\perp \\overline { d b } \\) and \\( d e = e b \\). calculate the…

Explanation:

Step1: Find the length of ( DE ) and ( EB )

Since ( DE = EB ) and ( DB=8) cm, then ( DE=\frac{DB}{2}=\frac{8}{2} = 4) cm.

Step2: Use the Pythagorean theorem to find ( CE )

In right - triangle ( CDE ), by the Pythagorean theorem (a^{2}+b^{2}=c^{2}), where (c = CD = 7) cm and (a = DE=4) cm. Let (b = CE), then (CE=\sqrt{CD^{2}-DE^{2}}=\sqrt{7^{2}-4^{2}}=\sqrt{49 - 16}=\sqrt{33}\approx5.7) cm.

Step3: Use the Pythagorean theorem to find ( AE )

In right - triangle ( ADE ), by the Pythagorean theorem, where (c = AD = 10) cm and (a = DE = 4) cm. Let (b = AE), then (AE=\sqrt{AD^{2}-DE^{2}}=\sqrt{10^{2}-4^{2}}=\sqrt{100 - 16}=\sqrt{84}\approx9.2) cm.

Step4: Calculate the length of ( AC )

Since (AC=AE + CE), then (AC\approx5.7+9.2 = 14.9) cm.

Answer:

(14.9)