Question

The bases of an isosceles triangle is 4/3 cm. the perimeter of the triangle is 4 2/15 cm. what is the length of eighter of the remaining equal sides?

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{\orange{Question}}}}}}$

The bases of an isosceles triangle is 4/3 cm. the perimeter of the triangle is 42/15 cm. what is the length of either of the remaining equal sides ?

$\Large{\underline{\underline{\mathfrak{\bf{\orange{Solution}}}}}}$

$\Large{\underline{\mathfrak{\bf{\blue{Given}}}}}$

• The bases of an isosceles triangle is 4/3 cm.
• the perimeter of the triangle is 42/15 cm

$\Large{\underline{\mathfrak{\bf{\blue{Find}}}}}$

• Length of remaining equal sides

$\Large{\underline{\underline{\mathfrak{\bf{\red{Explanation}}}}}}$

Let,

$:\mapsto\sf{\green{\:Base_{Isosceles\:triangle}\:=\:B}}\\ \\ :\mapsto\sf{\green{\:Equal\:side\:of\:isosceles\:triangle\:be\:=\:A}}$

Here, In diagram,

Isosceles triangle PQR ,

• PQ = RS , these are equal side
• QR is the Base of this triangle

$\large{\underline{\mathfrak{\bf{\blue{Formula}}}}}$

$\boxed{\underline{\sf{\orange{\:perimeter_{isosceles\:triangle}\:=\:(2A+B)}}}}$

keep above all values ,

$:\mapsto\sf{\:\dfrac{42}{15}\:=\:(2A+\dfrac{4}{3})} \\ \\ :\mapsto\sf{\:2A\:=\:\dfrac{42}{15}-\dfrac{4}{3}} \\ \\ :\mapsto\sf{\:2A\:=\:\dfrac{42-4\times5}{15}} \\ \\ :\mapsto\sf{\:2A\:=\:\dfrac{42-20}{15}} \\ \\ :\mapsto\sf{\:A\:=\:\dfrac{22}{15\times2}} \\ \\ :\mapsto\sf{\red{\:A\:=\:\dfrac{11}{15}\:cm}}$

$\Large{\underline{\mathfrak{\bf{\blue{Hence}}}}}$

• Value of equal side of isosceles triangle be = 11/15 cm

Or,

• PQ = RS = 11/15 cm.

___________________

Answer 2

⠀⠀⠀⠀ ⠀ $\red{\boxed{\sf{\blue{\:Given\:}}}}$ ⠀⠀

${\:The\:base\:of\:an\: isosceles\:triangle\:}\dfrac{4}{3}$...

⠀${\:The\:perimeter\:of\:an\: isosceles\:triangle\:}\dfrac{42}{15}...$

⠀⠀⠀⠀ ⠀$\red{\boxed{\sf{\blue{\:To\:find\:}}}}$ ⠀⠀

The length of either of the remaining equal sides...

⠀⠀⠀⠀⠀ $\red{\boxed{\sf{\blue{\:Solution\:}}}}$ ⠀⠀

Let the equal sides be x...

Let the base be y...

Perimeter of a triangle = sum of all sides...

• perimeter = AB + BC + CA

So...

perimeter = 2x + y

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀${\overbrace{\underbrace{\blue{AB\:=\:AC}}}}$

• ⠀ $\dfrac{42}{15} = ( 2x \:+\: \dfrac{4}{3})$

• ⠀ $\dfrac{42}{15}-\dfrac{4}{3} = 2x$

• ⠀⠀ $\dfrac{42 - 20}{15} = 2x$⠀

• ⠀⠀$\dfrac{22}{15} = 2x$⠀

• ⠀⠀$\dfrac{22}{15} = 2x$⠀⠀

• ⠀ ⠀$\dfrac{22}{15} = 2x$⠀ ⠀⠀

• ⠀⠀$\dfrac{22}{15\:×\:2} = x$⠀⠀

• ⠀⠀$\dfrac{22}{30} = x$⠀⠀

• ⠀ ⠀$\dfrac{11}{15} = x$⠀ ⠀⠀

⠀⠀⠀

AB = AC = x

Therefore, equal sides of isosceles triangle are...

---✁ $\</strong><strong>p</strong><strong>i</strong><strong>n</strong><strong>k</strong><strong>{\boxed{\sf{\orange{\</strong><strong>d</strong><strong>f</strong><strong>r</strong><strong>a</strong><strong>c</strong><strong>{</strong><strong>1</strong><strong>1</strong><strong>}</strong><strong>{</strong><strong>1</strong><strong>5</strong><strong>}</strong><strong>\:</strong><strong>cm</strong><strong>}}}}$ ⠀