Question

The longest side of a triangle is twice the shortest side and third side is 3 cm longer than shortest side. If perimeter of triangle is more than or equal to 203 cm then minimum length of the shortest side is: *​

Answer 1

Answer:

$\huge \mathfrak \orange{: :} \huge \mathfrak \pink{ answer}$

Let the length of shortest side = ‘x’ cm

According to the question,

The longest side of a triangle is twice the shortest side ⇒ Length of largest side = 3x

Also, the third side is 3 cm longer than the shortest side

⇒ Length of third side = (x + 3) cm Perimeter of triangle = sum of three sides

= x + 3x + x + 2 = 5x + 2 cm

Now, we know that, Perimeter is more than 166 cm

⇒ 5x + 2 ≥ 203

⇒ 5x ≥ 205

⇒ x ≥ 41

• Hence, minimum length of the shortest side should be 5 cm

Answer 2

Given :

• The longest side of a triangle is twice the shortest side
• Third side is 3cm longer than shortest side.
• Perimeter of triangle is more than or equal to 203cm

$\:$

To Find :

• Minimum length of the shortest side is ?

$\:$

Used Formula :

$\large \bf \red⇝ \: Perimeter \: _{(Triange)} \: = \: (a + b + c)$

$\:$

Solution :

Here,

The longest side of a triangle is twice the shortest side

Third side is 3cm longer than shortest side.

Let,

• Shortest side = x
• Longest side = 2x
• Third side = x+3

We know that,

$\large \bf \implies \: Perimeter \: _{(Triange)} \: = \: (a + b + c)$

And,

Perimeter of triangle is more than or equal to 203cm

So,

$\sf \implies \: 203cm \: ≤ \: x + 2x + x + 3$

$\sf \implies \: 203cm \:≤ \: 4x+ 3$

$\sf \implies \: 203 - 3\: ≤ \: 4x$

$\sf \implies \: 200\: ≤ \: 4x$

$\displaystyle\sf \implies \: \cancel\frac{200}{4} \: ≤ \: x$

$\displaystyle\sf \implies \: 50 \: ≤ \: x$

$\bf \red{\implies \: \underline{ \boxed{ \large\bf x \: ≥ \: 50}}}$

Hence,

❝ Minimum length of the shortest side is 50cm. ❞