Question

10. Each side of an isosceles triangle is 15 cm and perimeter of the triangle is 50 cm. Find the
third side



answer 100
​

Answer 1

✬ Third side = 20 cm ✬

Step-by-step explanation:

Given:

• Each side of isosceles triangle is of 15 cm.
• Perimeter of triangle is 50 cm.

To Find:

• What is the length of third side ?

Solution: Let the length of third side of isosceles triangle be x cm.

As we know that in an isosceles triangle two sides are equal to each other.

Therefore length of all three sides will be

• 1st side = 15 cm
• 2nd side = 15 cm
• 3rd side = x cm

★ Perimeter of ∆ = Sum of all sides ★

A/q

• Perimeter is 50 cm

$\implies{\rm }$ 50 = 15 + 15 + x

$\implies{\rm }$ 50 = 30 + x

$\implies{\rm }$ 50 – 30 = x

$\implies{\rm }$ 20 = x

Hence, length of third sides of triangle is 20 cm.

[ Verification ]

➟ 50 = Sum of all sides

➟ 50 = 15 + 15 + 20

➟ 50 = 50

$\large\bold{\texttt {Verified }}$

Answer 2

Answer:

$\setlength{\unitlength}{20mm}\begin{picture}(16,4)\thicklines\put(8.8,3){\large\sf{A}}\put(7.8,1){\large\sf{B}}\put(10.03,1){\large\sf{C}}\put(8,1){\line(1,0){2}}\put(8,1){\line(1,2){1}}\put(10,1){\line(-1,2){1}}\put(9.6,1.9){\sf{\large{15 cm}}}\put(7.8,1.9){\sf{\large{15 cm}}}\put(8.8,0.8){\sf{\large{? cm}}}\end{picture}$

• Each Equal Sides = 15 cm
• Perimeter of Triangle = 50 cm

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Perimeter=Sum\:of\:all\:Sides\\\\\\:\implies\sf Perimeter=AB+AC+BC\\\\\\:\implies\sf 50\:cm=15\:cm+15\:cm+BC\\\\\\:\implies\sf 50\:cm=30\:cm+BC\\\\\\:\implies\sf 50\:cm-30\:cm=BC\\\\\\:\implies\underline{\boxed{\sf BC=20\:cm}}$

⠀

$\therefore\:\underline{\textsf{Third Side of Isosceles Triangle is \textbf{20 cm}}}.$