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The base of an isosceles triangle is $43$ cm. The perimeter of the triangle is $4215$ cm. The length of either of the remaining equal sides is ____ cm.

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Detailed Solution

The base of an isosceles triangle is

43

cm. The perimeter of the triangle is

4215

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

cm.
Let

Δ A B C

as an isosceles triangle, whose base is

cm and other two sides be x cm.
Question Image

We know that the two sides of an isosceles triangle are equal, so AB=BC=x cm.
Perimeter is given as

4215

cm.
Converting mixed fraction into fraction.

P = 4 × 15 + 2 15 = 60 + 2 15 = 6215

Perimeter of triangle is given by sum of all sides of triangle.

P = x + x + 43

Substituting the given values in perimeter formula.

⇒ 6215 = 2 x + 43 ⇒ 2 x = 6215 − 43

Taking the LCM,

⇒ 2 x = 42 − 20 15 ⇒ 2 x = 4215 ⇒ x = 2115 ⇒ x = 75

Hence, the length of the remaining two sides is

cm.

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