Question

Find the perimeter of an equilateral triangle whose area is equal to area of other triangle with sides 21 16 and 16

Answer 1

Answer:

$\huge{\pink{\green{\sf{\therefore Perimeter\:of\:equilateral\:Triangle=51.3\:cm}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

▪In the given question information given about two Triangle whose areas are equal and one triangle is equilateral triangle.

▪We have to find Perimeter of equilateral triangle.

$\underline \bold{Given : } \\ \implies Area \: of \: 1st\: Triangle = Area \: of \: 2nd \: Triangle \\ \implies sides \: of \: 2nd \: Triangle = 21,16 \: and \: 16 \\ \\ \underline \bold{To \:Find : } \\ \implies Perimeter \: of \: 1st \: Triangle = ?$

▪According to given question :

$\bold{For \: 2nd \: Triangle :}\\ \implies s = \frac{a + b + c}{2} \\ \implies s = \frac{21 + 16 + 16}{2} \\ \implies s = \frac{53}{2} = 26.5 \\ \\ \underline\bold{by \: Heron's \: Formula : }\\ \implies Area \: of \: equilateral \: Triangle = Area \: of \: second \: Triangle \\ \implies Area = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies area = \sqrt{26.5(26.5 - 21)(26.5 - 16)(26.5 - 16)} \\ \implies Area = \sqrt{26.5 \times 5.5 \times 10.5 \times 10.5} \\ \implies Area = \sqrt{16.068.9375} \\ \implies Area = 126.76 {cm}^{2}$

▪We know the formula for Area of equilateral Triangle.

$\implies Area \: of \: equilateral \: Triangle = 126.76 {cm}^{2} \\ \implies \frac{ \sqrt{3} {side}^{2} }{4} = 126.76 \\ \implies {side}^{2} = \frac{126.76 \times 4}{1.732} \\ \implies {side} = \sqrt{292.74} \\ \bold { \implies side = 17.10 \: cm }\\ \\ \implies Perimeter \: of \: equilateral \: triangle = a + b + c \\ \implies Perimeter = 17.1 + 17.1 + 17.1 \\ \bold{\implies Perimeter = 51.3 \: cm}$

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