Question

The longest side of a triangle is three times the shortest side and the third side is three 3 cm.
shorter than the longest side. If the perimeter of the triangle is atleast 67cm. , find the
minimum length of the shortest side.

Answer 1

Step-by-step explanation:

here is the answer.hope it will help u

Answer 2

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

Given that,

The longest side of a triangle is three times the shortest side and the third side is three 3 cm shorter than the longest side.

So,

$\begin{gathered}\begin{gathered}\bf\: Let \: assume \: that-\begin{cases} &\sf{shortest \: side = x \: cm} \\ \\ &\sf{longest \: side = 3x \: cm}\\ \\ &\sf{third \:side = 3x - 3 } \end{cases}\end{gathered}\end{gathered}$

According to statement,

➢ The perimeter of triangle is atleast 67 cm.

It means,

➢ Sum of three sides of a triangle is atleast 67 cm

$\rm :\longmapsto\:x + 3x + 3x - 3 \geqslant 67$

$\rm :\longmapsto\:7x - 3 \geqslant 67$

On adding 3, on both sides, we get

$\rm :\longmapsto\:7x - 3 + 3\geqslant 67 + 3$

$\rm :\longmapsto\:7x \geqslant 70$

$\bf\implies \:x \geqslant \dfrac{70}{7}$

$\bf\implies \:x \geqslant 10 \:$

$\bf\implies \:Minimum \: length \: of \: shortest \: side \: = \: 10 \: cm$

Additional Information :-

$\boxed{ \bf{ \: |x| < y\bf\implies \: - y < x < y}}$

$\boxed{ \bf{ \: |x| \leqslant y\bf\implies \: - y \leqslant x \leqslant y}}$

$\boxed{ \bf{ \: |x| > y \: \bf\implies \:x < - y \: \: or \: \: x > y}}$

$\boxed{ \bf{ \: |x| \geqslant y \: \bf\implies \:x \leqslant - y \: \: or \: \: x \geqslant y}}$

$\boxed{ \bf{ \: x > - y \: \bf\implies \: - x < y}}$

$\boxed{ \bf{ \: x < - y \: \bf\implies \: - x > y}}$

$\boxed{ \bf{ \: x \geqslant - y \: \bf\implies \: - x \leqslant y}}$

$\boxed{ \bf{ \: x \leqslant - y \: \bf\implies \: - x \geqslant y}}$