Question

An equilateral triangle has a side labeled 3x. The perimeter of the triangle is 99 cm. what is the measure of the sides of the triangle?​

Answer 1

$\underline{\underline{\frak{\qquad Given :\qquad}}}$

• An equilateral triangle has a side labeled 3x. The perimeter of the triangle is 99 cm.

$\underline{\underline{\frak{\qquad To\:Find :\qquad}}}$

• The measure of the sides of the traingle = ?

$\underline{\underline{\frak{\qquad Solution :\qquad}}}$

• An equilateral triangle has a side labeled 3x.
• Perimeter of an equilateral traingle = 99 cm

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies \sf Perimeter_{(of \: equilateral \: \Delta)} = 3a$

$:\implies \sf 99 = 3(3x)$

$:\implies \sf 99 = 9x$

$:\implies \sf x = \dfrac{99}{9}$

$:\implies \sf x = 11 \: cm$

$\bigstar \: \underline{\textsf{The measure of the sides of the equilateral traingle :}}$

$\dashrightarrow\:\:\sf Side_{(of \: equilateral \: \Delta)} = 3x$

$\dashrightarrow\:\:\sf Side_{(of \: equilateral \: \Delta)} = 3(11)$

$\dashrightarrow\:\: \underline{ \boxed{\sf Side_{(of \: equilateral \: \Delta)} = 33 \: cm}}$

$\therefore\:\underline{\textsf{The measure of the sides of the traingle is \textbf{33 cm}}}.$

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$\underline{\underline{\frak{\qquad Verification :\qquad}}}$

$\longrightarrow\: \sf 99 = 3(3x)$

$\longrightarrow\: \sf 99 = 3(3 \times 11)$

$\longrightarrow\: \sf 99 = 3(33)$

$\longrightarrow\: \underline{ \boxed{\sf 99 = 99}}$

$\longrightarrow\: \underline{ \boxed{\sf LHS = RHS}}$

$\underline{\underline{\frak{\qquad Hence, Verified\qquad}}}$

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