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# Help with geo

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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?

May 2, 2023

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The side length of the square PZXY is sqrt(2).

Step-by-step explanation:

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.

We have,

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

Therefore,

The side length of the square PZXY is √2.

May 2, 2023