Question

Two equal sides of a triangle are each 3 m less than the twice of third side. if the perimeter of a triangle is 34 m, find the length of the third side.


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Answer 1

$\textbf{Given:}$

$\textsf{Two equal sides of a triangle are each 3 m less than}$

$\textsf{the twice of third side}$

$\textbf{To find:}$

$\textsf{Length of the third side}$

$\textbf{Solution:}$

$\textsf{Let the length of the third side be x m}$

$\textsf{Then, the length of equal side is 2x-3 m}$

$\textsf{Perimeter of the triangle = 34 m}$

$\mathsf{(2x-3)+(2x-3)+x=34}$

$\mathsf{5x-6=34}$

$\mathsf{5x=34+6}$

$\mathsf{5x=40}$

$\mplies\mathsf{x=\dfrac{40}{5}}$

$\mplies\boxed{\mathsf{x=8}}$

$\textbf{Answer:}$

$\textsf{Length of the third is 8 m}$

$\textbf{Find more:}$

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Sides of the triangle are 13cm, 14cm and 15 cm, find the length of thesmallest altitude of the triangle.

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Answer 2

Given info : Two equal sides of a triangle are each 3m less than the twice of 3rd side.

To find : if the perimeter of a triangle is 34 m, find the length of the 3rd side.

solution : Let a , a and b are three sides of a triangle [ says two sides are equal so we assume three sides are a , a and b. ]

a/c to question,

Two equal sides of a triangle are each 3m less than the twice of 3rd side.

⇒a = 2b - 3 .....(1)

now perimeter of triangle = sum of length of sides

⇒34 = a + a + b = 2a + b

⇒34 = 2(2b - 3) + b [ from eq (1). ]

⇒34 = 4b - 6 + b

⇒34 + 6 = 5b

⇒b = 8

Therefore the length of 3rd side = b = 8 m