Question

The length of each of the two equal sides of an isosceles triangle is 2 cm less than twice the length of the third side. Find the dimensions of the triangle if its perimeter is 36 m. ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that, the length of each of the two equal sides of an isosceles triangle is 2 cm less than twice the length of the third side.

Let assume that triangle ABC is an isosceles triangle such that AB = AC.

Let assume that

Length of BC = x

So, AB = 2x - 2

So, AC = 2x - 2

Now, further given that Perimeter of triangle ABC = 36 m

$\rm \: AB+BC+CA = 36$

$\rm \: 2x - 2 + 2x - 2 + x = 36$

$\rm \: 5x - 4 = 36$

$\rm \: 5x = 36 + 4$

$\rm \: 5x = 40$

$\bf\implies \:x \: = \: 8$

Hence, Dimensions of triangle ABC is

AB = 2x - 2 = 2 × 8 - 2 = 14 cm

AC = 2x - 2 = 2 × 8 - 2 = 14 cm

AC = x = 8 cm

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

Given,

The length of each of the two equal sides of an isosceles triangle is 2 cm less than twice the length of the third side.

Let us assume that ∆ABC is an isosceles triangle such that AB = AC.

Let us assume that

Length of BC = x m

AB = (2x - 2)m

AC = (2x - 2)m

Also, given that Perimeter of ∆ABC = 36 m

$\tt⇢ \: \: x + 2x - 2 + 2x - 2 = 36$

$\tt⇢ \: \: 5x - 4 = 36$

$\tt⇢ \: \: 5x = 40$

$\tt⇢ \: \:x = \cancel \frac{40}{5}$

$\tt⇢ \: \: x = 8m$

Then, Dimensions of ∆ABC are :

BC = x = 8m

AB = (2x - 2) = 2(8) - 2 = 14m

AC = (2x - 2) = 2(8) - 2 = 14m

FINAL ANSWER :

THE DIMENSIONS ARE 8m , 14m , 14m .