Question

the perimeter of an isosceles triangle is 30 cm The length of its congruent sides is 3cm ​

Answer 1

${ \bold { \underline{\large\purple{Correct \: Question : - }}}} \:$

The perimeter of an isosceles triangle is 30 cm .The length Of its congruent sides is 3cm more than its base .find the length of all the side.

${ \bold { \underline{\large\pink{Given : - }}}} \:$

★ Perimeter of an isosceles triangle is 30 cm

★ The length of its congruent sides is 3cm .

${ \bold { \underline{\large\pink{Find: - }}}} \:$

★ Find the length of all the side.

${ \bold { \underline{\large\purple{Diagram : - }}}} \:$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

${ \bold { \underline{\large\purple{Solution : - }}}} \:$

So , Lets consider the base side be " x " then the congruent sides be ( x + 3 )

Now,

We know the perimeter of Triangle = Sum of all sides

(x + 3) + (x + 3) + x = 30

↬ 3x + 6 = 30

↬3x = 30 - 6

↬ 3x = 24

↬ x = 24/3

$\longmapsto\tt{x=\cancel\dfrac{24}{3}}$

↬x = 8 cm

Then,

• Base side = x

= 8 cm

• Congruent sides = ( x + 3 )

= ( 8 + 3 )

= 11 cm

Note :-

➤ Kindly see the diagram from site. (brainly.in)

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Answer 2

Correct Question :-

The perimeter of an isosceles triangle is 30 cm. The length of each congruent side is 3cm more than the length of its base. Find the lengths of all the sides.

Solution :-

$\huge\orange{\sf{⇝Given:-}}$

• The perimeter of an isosceles triangle is 30 cm.
• Length of each congruent side 3cm more than the length of its base.

$\huge\orange{\sf{⇝Let:-}}$

• $\text{Let~the~base~be~x}$
• $\text{Congruent~sides = x+3 }$

$\huge\orange{\sf{⇝We~know~that:-}}$

Perimeter of an isosceles triangle = 2×Side + Base

$\sf\therefore{2×(x+3)+x}$

$\sf\leadsto{2×(x+3)+x}$

$\sf\leadsto{2x+6+x}$

$\sf\leadsto{3x+6}$

Also,

Also,Perimeter of the isosceles triangle = 30 cm(Given)

Therefore;

$\sf\leadsto{3x+6=30cm}$

$\sf\leadsto{3x=(30-6)cm}$

$\sf\leadsto{3x=24cm}$

$\sf\leadsto{x=\cancel\frac{24}{3}}$

$\sf\leadsto{x=8cm}$

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Then;

$\tt{The~Base=x=8cm}$

$\tt{The~Congruent~Sides=x+3=11cm}$

$\small\bf\therefore{\red{The~sides~of~the~isosceles~triangle~are~11cm,11cm~and~8cm}}$