Answer:
The length of BW is [tex]105\sqrt{2}[/tex], or about 148.49.
Step-by-step explanation:
For this problem, we will assume that the figure is a square. We will call the figure "Figure BOWL".
Because figure BOWL is a square, we know that the lengths of each sides of the square are equal, so the length of each side is 105.
Notice that the BW, OB, and WO make a triangle. We'll call it triangle BOW. Since figure BOWL is a square, we know that angle BOW is 90°, and so triangle BOW is a right triangle.
Since triangle BOW is a right triangle, we can solve for BW using the Pythagorean theorem, [tex]a^{2} + b^2 = c^2[/tex]. "a" and "b" are the legs of the triangle, while "c" is the hypotenuse of the triangle.
In triangle BOW, the legs are OB and WO, while the hypotenuse is BW.
Plug in the values for the equation and solve.
[tex]a^2 + b^2 = c^2[/tex]
[tex]OB^2 + WO^2 = BW^2[/tex]
[tex]105^2 + 105^2 = BW^2[/tex]
[tex]11,025 + 11,025 = BW^2[/tex]
[tex]22,050 = BW^2[/tex]
[tex]\sqrt{22,050} = BW[/tex]
We can either use the estimated value, or the exact simplified value of [tex]\sqrt{22,050}[/tex].
Here is the exact simplified value:
[tex]\sqrt{22,050} = \sqrt{25 * 882} = \sqrt{25 * 9 * 98} = \sqrt{25 * 9 * 49 * 2} = \sqrt{5^2 * 3^2 * 7^2 * 2} = (5 * 3 * 7)\sqrt{2} = 105\sqrt{2}[/tex]
BW = [tex]105\sqrt{2}[/tex]
For the estimated value, just use a calculator:
[tex]\sqrt{22,050}[/tex] ≈ 148.49
BW ≈ 148.49
