A diagram is shown where RT=12 and WT=5 Complete the statements. Delta TWR will have an area equal to: To show the Pythagorean theorem, a square that is drawn on the hypotenuse of WT+RT. (WT+RT)^2 the sum of the area of square WMXT and the area of square RTKD. 2. The length of each side of the square that is drawn with side overline (RW) is __ . 3. Delta WKB is shown where WK=sqrt (65) and WB=4 Find the exact length of overline (BK) 4. A right triangle has side lengths of sqrt (35) and sqrt (52) Find the exact length of the hypotenuse.

Let's address each statement step by step:1. To show the Pythagorean theorem, a square that is drawn on the hypotenuse of \(\triangle T W R\) will have an area equal to:- \(W T+R T\) is incorrect because it's just the sum of the lengths, not the areas.- \((W T+R T)^{2}\) is incorrect because it's the square of the sum of the lengths, not the sum of the areas of the squares on the legs.- the sum of the area of square WMXT and the area of square RTKD is correct because according to the Pythagorean theorem, the area of the square on the hypotenuse (RW) is equal to the sum of the areas of the squares on the other two sides (WT and RT).Answer: the sum of the area of square WMXT and the area of square RTKD.2. The length of each side of the square that is drawn with side \(\overline{R W}\) is:To find the length of RW, we use the Pythagorean theorem for triangle \(\triangle T W R\):\(RW^2 = WT^2 + RT^2\)\(RW^2 = 5^2 + 12^2\)\(RW^2 = 25 + 144\)\(RW^2 = 169\)\(RW = \sqrt{169}\)\(RW = 13\)Answer: The length of each side of the square that is drawn with side \(\overline{R W}\) is 13.3. \(\triangle W K B\) is shown where \(W K=\sqrt{65}\) and \(W B=4\). Find the exact length of \(\overline{B K}\).Since \(\triangle W K B\) is a right triangle with \(\angle B\) as the right angle, we can use the Pythagorean theorem to find \(BK\):\(WB^2 + BK^2 = WK^2\)\(4^2 + BK^2 = (\sqrt{65})^2\)\(16 + BK^2 = 65\)\(BK^2 = 65 - 16\)\(BK^2 = 49\)\(BK = \sqrt{49}\)\(BK = 7\)Answer: The exact length of \(\overline{B K}\) is 7.4. A right triangle has side lengths of \(\sqrt{35}\) and \(\sqrt{52}\). Find the exact length of the hypotenuse.Again, we use the Pythagorean theorem:\(hypotenuse^2 = (\sqrt{35})^2 + (\sqrt{52})^2\)\(hypotenuse^2 = 35 + 52\)\(hypotenuse^2 = 87\)\(hypotenuse = \sqrt{87}\)Answer: The exact length of the hypotenuse is \(\sqrt{87}\).