$X O Y Z$ is a rectangle with vertices $X(-3,0), O(0,0)$, $\mathrm{Y}(0,4)$ and $\mathrm{Z}(x, y)$. The length of its each diagonal is
Explanation
The length of the diagonal of a rectangle is given by sqrt(length^2 + breadth^2). Here, length = 4 units and breadth = x units. So, the length of the diagonal is sqrt(4^2 + x^2) = sqrt(16 + x^2) = sqrt(x^2 + 16) units. This is equal to sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 units. Therefore, x^2 + 16 = 25, which gives x^2 = 9, and x = 3 units. So, the length of the diagonal is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 units.
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