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The lengths of the medians through acute...

The lengths of the medians through acute angles of a right-angled triangle are 3 and 4. Find the area of the triangle.

Text Solution

Verified by Experts

AD=3
CE=4
Apollonian theorem
`(AB)^2+(AC)^2=2((AD)^2+(BD)^2)`
`b^2+c^2=2(9+a_2/4)-(1)`
`b^2+a^2=2(c^2/4+16)-(2)`
`b^2=a^2+c^2`
`2b^2+a^2+c^2=2(a^2/4+c^2/4+25)`
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Knowledge Check

  • If one of the acute angles of a right - angled triangle is 55^(@) , what is the measure of the other acute angle ?

    A
    `40^(@)`
    B
    `30^(@)`
    C
    `25^(@)`
    D
    `35^(@)`

  • If the sum of lengths of the hypotenuse and another side of a right angled triangle is given, show that the area of the triangle is max. when, the angle between these is

    A
    `pi/12`
    B
    `pi/4`
    C
    `pi/3`
    D
    `pi/2`

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