Question

the length of two equal sides of an isosceles triangle is 4meter less than twice the length of the third side , find the dimensions of the triangle if its perimeter is 57 m

Answer 1

let length of the unique side be x
ATQ
2x-4+2x-4+x=57
5x-8=57
5x=65
x=13
......
unique side= x = 13m
equal sides = 2x-4 = 26-4 = 22m (each)

Answer 2

The dimensions of the isosceles triangle are 22 m, 22 m and 13 m respectively.

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Let's understand a few concepts:

To solve the given problem we will use the following formula:

$\boxed{\bold{Perimeter\:of\:a\:triangle = sum\:of\:all\:3 \:sides}}$

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Let's solve the given problem:

Let's say the 3rd side of the isosceles triangle is "x" meter.

The length of two equal sides of an isosceles triangle is 4meter less than twice the length of the third side, so, we get

The length of the two equal sides of the isosceles Δ = (2x - 4) meter

The perimeter of the isosceles Δ = 57 m

By using the above formula, we can form an equation as,

$(2x - 4)+(2x -4 )+(x) = 57$

$\implies 2x - 4 + 2x - 4 + x = 57$

$\implies 4x - 8 + x = 57$

$\implies 5x - 8 = 57$

$\implies 5x = 57 + 8$

$\implies 5x = 65$

$\implies x = \frac{65}{13}$

$\implies \bold{x = 13 \:m}$ ← length of 3rd side

∴ The length of each of the two equal sides is,

= $(2x - 4) \:m$

= $(2\times 13 - 4) \:m$

= $(26 - 4) \:m$

= $\bold{22\:m}$

Thus, the length of each of the two equal sides is 22 m and the length of the 3rd side is 13 m.

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