Question

.The base of an isosceles triangle is 6 cm and its perimeter is 16 cm. The length of each of the equal sides is *



5 cm

8 cm

10 cm

22 cm

​

Answer 1

(A) 5 CM

Base 6 cm
Perameter 16 cm

P=2a+b

Answer 2

$\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Given :-}}}}}}$

• ➬ Base of isosceles triangle = 6 cm
• ➬ Perimeter of triangle = 16 cm

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large\underline{\underline{\maltese{\gray{\pmb{\sf{\: To \: Find :-}}}}}}$

• ➬ The length of each equal sides = ?

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large\underline{\underline{\maltese{\orange{\pmb{\sf{\: Solution :-}}}}}}$

❒ Formula Used :

$\large{\blue{\bigstar}}{\underline{\boxed{\red{\sf{Perimeter{\small_{(Triangle) }} = a + b + c}}}}}$

➢Here :

• ➳ Perimeter = 16 cm
• ➳ A = Side 1 = 6 cm
• ➳ B = Side 2 = y
• ➳ C = Side 3 = y

$\qquad{━━━━━━━━━━━━━━}$

❒ Length of equal sides :

$\qquad{\leadsto{\sf{Perimeter = a + b + c}}}$

$\qquad{\leadsto{\sf{16 = 6 + y + y}}}$

$\qquad{\leadsto{\sf{16 - 6= y + y}}}$

$\qquad{\leadsto{\sf{10= 2y}}}$

$\qquad{\leadsto{\sf{ \dfrac{10}{2} = y}}}$

$\qquad{\leadsto{\sf{ \cancel\dfrac{10}{2} = y}}}$

$\large\qquad{\color{maroon}{:\twoheadrightarrow{\underline{\boxed{\sf{y = 5 \: cm}}}}}}{\pink{\bigstar}}$

$\qquad{━━━━━━━━━━━━━━}$

❒ Therefore :

❝ Length of equal sides is 5 cm. ❞

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large\underline{\underline{\maltese{\pink{\pmb{\sf{\:Verification :-}}}}}}$

${:\longmapsto{\sf{ a + b + c = perimeter }}}$

${:\longmapsto{\sf{ 6 + y + y = 16 \: cm}}}$

${:\longmapsto{\sf{ 6 + 5 + 5 = 16 \: cm}}}$

${:\longmapsto{\sf{ 6 + 10 = 16 \: cm}}}$

${:\longmapsto{\sf{ 16 \: cm = 16 \: cm}}}$

${:\longmapsto\red{\underline{\sf{LHS = RHS }}}}$

Hence, Verified.

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