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Reaper534
Quadrilateral WXZY is a square. If YX = 30 and WT = 2x – 7, then find the value of x.
|dw:1361427838657:dw| WT?? I assume you mean WY. I drew a picture of a square. You see that diagonal line segment? It's 30, like the problem tells us. ***Here's a big geometry rule*** In a square, all sides are equal in length. Okay. So do you see how I cut the square into two triangles, by drawing that diagonal? Let's just look at ONE of the triangles. The HYPOTENUSE of the triangle is 30. We need to find the length of each of its LEGS. Remember the PYTHAGOREAN THEORUM? \[a^{2}+b^{2}=c^{2}\] A and B are the LEGS. C is the HYPOTENUSE. We already know that the HYPOTENUSE is 30. So.... \[a^{2}+b^{2}=900\] (Because 30 squared is 900) Now, since the LEGS of the square are both EQUAL, we know that....\[a^{2}=b^{2}\] QUESTION: What two numbers, added together, would equal 900? ANSWER: 450 So.... \[a^{2}=450\] \[b^{2}=450\] QUESTION: What's the square root of 450? ANSWER: 21.21 So... A and B both equal 21. Take another look at the square I drew for you. We now know that.... 2x - 7 = 21 Now, can you solve for X?
You could take the approach that the diagonals of a square are congruent which would make WX = XY. Also, a square is a parallelogram and the diagonals of a parallelogram bisect each other. So WT = 1/2 of WZ. 2*WT = WZ 2* (2x - 7) = 30 Sove for x. Post your answer here if you'd like someone to check it. Thanks. @Reaper534