Question

the figure is a kite. what is the length of the kites longer diagonal? 5 units 35 units 40 units 48 units

Explanation:

Step1: Use Pythagorean theorem for upper right triangle

Let the half - length of the shorter part of the longer diagonal be \(x\). For the upper right triangle with hypotenuse \(13\) and one side \(12\), by \(a^{2}+b^{2}=c^{2}\), we have \(x=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\).

Step2: Use Pythagorean theorem for lower right triangle

Let the half - length of the longer part of the longer diagonal be \(y\). For the lower right triangle with hypotenuse \(37\) and one side \(12\), by \(a^{2}+b^{2}=c^{2}\), we have \(y=\sqrt{37^{2}-12^{2}}=\sqrt{1369 - 144}=\sqrt{1225}=35\).

Step3: Calculate the length of the longer diagonal

The length of the longer diagonal \(d=x + y\). Substitute \(x = 5\) and \(y = 35\) into the formula, \(d=5+35 = 40\).

Answer:

40 units