Area and Perimeter Practice Test 1

Question : 11 of 40

Marks: +1, -0

An equilateral triangle, a square and a circle have equal perimeters. If T denotes the area of the triangle, S, the area of the square and C, the area of the circle then,

C < S < T
T < S < C
T < C < S
S < T < C

Validate

Solution:

Let perimeter of each shape be x;
Then, side of the equilateral triangle =

x/3

Since, area of the equilateral triangle, T =

√3/4 ×(x/3)^2

x^2{12√3}

Again side of the square =

x/4

So, area of the square, S =

(x/4)^2

x^2/{16}

And, radius of circle =

{x×7}/{2×22}

{7x}/{44}

Therefore, area of the circle, C =

{22}/7 × {7x}/{44} × {7x}/{44}

{7x^2}/{88}

Hence, C > S > T.

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