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Show that in a right angled triangle, t...

Show that in a right angled triangle, the hypotenuse is the longest side.

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Let us consider a right-angled triangle ABC, right-angled at B.
In `∆ABC`,
`∠A + ∠B + ∠C = 180^@`(Angle sum property of a triangle)
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Show that in a right triangle the hypotenuse is the longest side.GIVEN : A right triangle ABC in which /_ABC=90^(@). TO PROVE : Hypotenuse AC is the longest side,i.e.AC>AB( ii) AC>BC

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Knowledge Check

  • The maximum area of a right angled triangle with hypotenuse h is :

    A
    `h^(2)/(2sqrt(2))`
    B
    `h^(2)/2`
    C
    `h^(2)/sqrt(2)`
    D
    `h^(2)/4`

  • In a right-angled triangle with sides a and b, hypotenuse c, the altitude drawn on the hypotenuse is x. Then

    A
    `ab=x^(2)`
    B
    `(1)/(a)+(1)/(b)=(1)/(x)`
    C
    `a^(2)+b^(2)=2x^(2)`
    D
    `(1)/(a^(2))+(1)/(b^(2))=(1)/(x^(2))`

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    The maximum area of a right angled triangle with hypotenuse h is

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    Fill in the blanks . (a) Each angle of an equilateral triangle measures ………….. (b) Medians of an equilateral triangle are …… (c) In a right triangle, the hypotenuse is the ……. Side.

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