Question

in triangle ABC seg CD is the median .If AC² + BC²=290
and CD=9 then AD= - -​

Answer 1

Answer:

The length of AD is 8 cm.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

In figure, in ΔABC, CD is a median. - - [ Given ]

∴ AC² + BC² = 2CD² + 2AD² - - [ Appllonius theorem ]

→ 290 = 2 ( 9 )² + 2AD²

→ 290 = 2 × 81 + 2AD²

→ 290 = 162 + 2AD²

→ 290 - 162 = 2AD²

→ 128 = 2AD²

→ AD² = 128 ÷ 2

→ AD² = 64

→ AD = √64 - - [ Taking square roots ]

∴ AD = 8 cm.

Additional Information:

1. Appllonius theorem:

1. This is a theorem related to median and the sides of a triangle.

2. This theorem is given by Mathematician Appllonius.

3. This theorem says that,

In a triangle, if median is drawn to one side, the sum of squares of remaining sides is equal to the sum of twice of squares of median and half of the third side.

Learn more:

https://brainly.in/question/17461016