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densk [106]
3 years ago
10

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

Mathematics
1 answer:
wariber [46]3 years ago
8 0

Answer:

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

Step-by-step explanation:

The distance between the line joining points A (<em>-b, c</em>) and C (<em>a, o</em>) 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.

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