If AOBC is a rectangle whose three vertices are A (0, 3), O (0, 0) and B (5, 0), then the length of its diagonal is

We have three vertices;

A = (0, 3)

O = (0, 0)

B = (5, 0)

Now,

As we know that diagonals of a rectangle are of equal length,

So,

Length of the diagonal AB = Distance between the points A and B

Calculate the distance between the points (x_{1}, y_{1}) and (x_{2}, y_{2});

By the formula;

We have;

d^{2} = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

x_{1} = 0, x_{2} = 5

y_{2} = 3, y_{2} = 0

d^{2} = (5 – 0)^{2} + (0 – 3)^{2}

d = √(25 + 9)= √34

Distance between A (0, 3) and B (5, 0) is √34

Hence, the required length of its diagonal is √34

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