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The perimeter of an equilateral triangle...

The perimeter of an equilateral triangle is `60 m`. The area is

A

`10sqrt3" "m^(2)`

B

`15sqrt3" "m^(2)`

C

`20sqrt3" "m^(2)`

D

`100sqrt3" "m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let each side of an equilateral be `x.`
Then, perimeter of an equilateral triangle `= 60 m`
`therefore x+x+x=60rArr3x=60rArrx(60)/(3)=20m`
`"Area of an equilateral triangle"=(sqrt3)/(4)("Side")^(2)=(sqrt3)/(4)xx20xx20=100sqrt3 m^(2)`
`"Thus, the area of triangle is"" "100sqrt3m^(2)`.
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Knowledge Check

  • The perimeter of an equilateral triangle is 60m. The area is

    A
    `10sqrt(3)m^(2)`
    B
    `15sqrt(3)m^(2)`
    C
    `20sqrt(3)m^(2)`
    D
    `100sqrt(3)m^(2)`

  • the area of an equilateral triangle is .

    A
    `(sqrt(3))/(4)a^(2)sq` units
    B
    `2a^(2)` sq units
    C
    `3sqrt(3)a^(2)` sq units
    D
    `(sqrt(3))/(2)a^(2)` sq units

  • The perimeter of an equilateral triangle is 60 cm. Find its (i) area and (ii) height. (Given, sqrt(3) = 1732 .)

    A
    `17.32` cm
    B
    `12.32` cm
    C
    `14.32` cm
    D
    `16.32` cm

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