Question

Two equal sides of an isosceles triangle are each 2 cm more than thrice the third side. If the perimeter of triangle is 67 cm, find the lengths of its sides.​

Answer 1

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$\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}$

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$\sf{\underline{\green{AnswEr:-}}}$

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• Third side of rectangle = 9 Cm

• Second side of rectangle = 29 Cm

• First side of rectangle = 29 Cm

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$\sf{\underline{\green{Given:-}}}$

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• Two equal sides of an isosceles triangle are each 2 cm more than thrice the third side. If the perimeter of triangle is 67 cm.

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$\sf{\underline{\green{Find:-}}}$

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• Find the lengths of its sides.

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$\sf{\underline{\green{Explanation:-}}}$

Let the third side be y.

$\:\:\:\:\dag\bf{\underline{\underline \red{Then:-}}}$

• First Side = (3y + 2)
• Second Side = (3y + 2)

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$\:\:\:\:\dag\bf{\underline{\underline \red{As\:we\:know\: that:-}}}$

$\small\pink{\underline {\boxed{\sf\pink{ Perimeter\:of\:a\:\triangle = Sum\:of\: three\: sides } }}}$

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$\sf{\underline\purple{A.T.Q:-}}$

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$\longrightarrow \sf {y + (3y + 2) + (3y + 2) = 67}$

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$\longrightarrow \sf {y + 2 \times (3y + 2) = 67}$

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$\longrightarrow \sf {y + 6y + 4 = 67}$

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$\longrightarrow \sf {7y = 67 - 3}$

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$\longrightarrow \sf {7y = 63}$

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$\longrightarrow \sf {y = \cancel\dfrac{63}{7} }$

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$\longrightarrow \sf {y = 9}$

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$\:\:\:\:\dag\bf{\underline{\underline \red{Hence:-}}}$

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• Third side of rectangle = 9 Cm

• Second side of rectangle = 3 × 9 + 2
• Second side of rectangle = 29 Cm

• First side of rectangle = 3 × 9 + 2
• First side of rectangle = 29 Cm

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$\rule{200}{2}$

Answer 2

Given:-

☆Two equal sides of an isosceles triangle are 2cm more than thrice the third side.

☆Perimeter of the triangle=67cm

To find:-

☆Length of the sides of the triangle

Solution:-

=>Let the third side of the triangle be x cm

=>Thus,the other two equal sides=(3x+2)cm

We know that:-

=>Perimeter of a triangle=Sum of 3 sides

Now:-

=>x + (3x+2) + (3x+2) = 67

=>x + 2(3x+2) = 67

=>x + 6x +4 = 67

=>7x = 67-3

=>7x=63

=>x=63/7

=>x=9

Thus,the sides of the triangle are:-

•9cm

•3×9+2=29cm

•3×9+2=29cm