Hello need help with geo
Points X, Y, and Z are on the sides QR , PR, and PQ respectively, of right triangle PQR such that PZXY is a square. If PQ=10 and PR=10, then what is the side length of the square?
The side length of the square PZXY is sqrt(2).
What is a square?
A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
Since triangle PQR is a right triangle, we can use the Pythagorean theoremto find the length of QR:
QR² = PQ² + PR²
QR² = 1² + 1²
QR² = 2
QR = √2
Since PZXY is a square, its sides are equal in length.
Let's denote the length of one side of the square as s.
Then, we can write:
PR = PX + RX
1 = s + QY
Since QY = PZ = s and PX = QX = QR - QY = sqrt(2) - s,
we can substitute these values into the equation for PR to get:
1 = s + (√2 - s)
1 = √2
The side length of the square PZXY is √2.