Question

AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.

Options

• 5

• 3

• `sqrt(34)`

• 4

Answer 1

AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is `underlinebb(sqrt(34))`.

Explanation:

The three vertices are: A = (0, 3), O = (0, 0), B = (5, 0)

We know that, the diagonals of a rectangle are of equal length,

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

Distance formula: d² = (x₂ – x₁)² + (y₂ – y₁)²

According to the question,

We have,

x₁ = 0, x₂ = 5

y₁ = 3, y₂ = 0

d² = (5 – 0)² + (0 – 3)²

d = `sqrt((5 - 0)^2 + (0 - 3)^2`

d = `sqrt(25 + 9)`

= `sqrt(34)`

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

Therefore, the length of its diagonal is `sqrt(34)`