Question

Which of the following represent the length of a diagonal of this trapezoid?

A
B
C
D

Answer 1

`\sqrt{\left(a+b\right)^(2)+c^(2)}`

Explanation:

The distance between the line joining points A (-b, c) and C (a, o) will be the length of the diagonal of given trapezoid.

Now,
`x_(1) = - b,\ y_(1) = c\ and\ x_(2) = a, y_(2) = 0`

Now, using distance formula,

AC =
`\sqrt{\left (x_(2)-x_(1)\right )^(2)+\left (y_(2)-y_(1)\right )^(2)}`

AC =
`\sqrt{\left(a-(-b) \right)^(2)+\left(0-c\right)^(2)}`

AC =
`\sqrt{\left(a+b\right)^(2)+\left(-c\right)^(2)}`

AC =
`\sqrt{\left(a+b\right)^(2)+c^(2)}`

Therefore, the length of diagonal AC of trapezoid =
`\sqrt{\left(a+b\right)^(2)+c^(2)}`

So, option (4) is the right option.