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 = (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 * 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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