Question

Two equal sides of a triangle are each 5 meters less than twice the third side.if the perimeter of the triangle is 85 meters,find the length of its sides.​

Answer 1

Answer:

Two equal sides of triangle  are 33 meters long each and the third side is 19 meters long.

Step-by-step explanation:

Let the two equal sides be x and the third side be y.

• x= 2y-5
• x=2y-5 (Because 2 sides are equal)

Perimeter given is 55m

• x+x+y = 85m.
• 2x+y = 85m.------------------------(1st equation)

Substitute x in eqn. (1)

• 2*(2y-5) +y = 85
• 4y-10+y = 85
• 5y -10 =85
• 5(y-2) = 5*17

On the LHS and RHS,5 gets ruled off.

• y-2 = 17

• y = 17+2 = 19 meters.

Now, Substitute y in x,

• x = 2y - 5
• x = 2*(19) - 5

• x = 38 -5

• x = 33 meters.

Therefore, two sides of the triangle are 33 meters and the side of the triangle is 19 meters.

Now, if we add all the three sides, we must get 85 meters. Thus, Confirming the values obtained

33+33+19 = 85 meters.

Answer 2

$\large\bf\underline{Length\:of\:sides:}$

ㅤㅤㅤㅤㅤ$\bigstar\boxed{\large\bf{⟼33cm,\:33cm,\:19cm}}$

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$\large\bf\underline{Given:}$ㅤ

• Two equal sides of a triangle are each 5 meters less than twice the third side

❒ Let the third side of triangle be x, then according to question the length of 2 similar sides will be :

ㅤㅤㅤㅤㅤ$\bf{⟼2x-5}$ㅤ— (1)

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• Perimeter = 85 cm

$\underline{\boxed{\bf\pink{Perimeter=sum\:of\:all\:sides}}}$

$\large\bf\underline{Therefore,\: putting\:the\: values:}$

ㅤㅤㅤㅤㅤ$\bf{⟼x+(2x-5)+2x-5)=85}$

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ㅤㅤㅤㅤㅤ$\bf{⟼x+2x+2x-5-5=85}$

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ㅤㅤㅤㅤㅤ$\bf{⟼5x-10=85}$

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ㅤㅤㅤㅤㅤ$\bf{⟼5x=85+10}$

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ㅤㅤㅤㅤㅤ$\bf{⟼x=\large\frac{95}{5}}$

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ㅤㅤㅤㅤㅤ$\bf{⟼x=19}$

$\bf{Hence,\:length\:of\:one\:side(x)=19cm}$

⟼ Putting the value of x in equation (1) to obtain the values of other sides

ㅤㅤㅤㅤㅤ$\bf{\implies 2x-5}$

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ㅤㅤㅤㅤㅤ$\bf{\implies (2\times 19)-5}$

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ㅤㅤㅤㅤㅤ$\bf{\implies 38-5}$

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ㅤㅤㅤㅤㅤ$\bf{\implies 33cm}$

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