Question

one of the equal sides of an iso celes triangle is 15 cm and its perimeter is 50cm fund the area of the triangle
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Answer 1

Question :

• One of the equal sides of an isoceless triangle is 15 cm and its perimeter is 50cm find the area of the triangle ?

Answer :

• The area of given triangle is 50√5 sq cm.

Solution :

• Given two sides of triangle are 15,15
• Let, other side be x.

Perimeter of ∆ = sum of all sides

$\implies \: 50cm \: = 15 + 15 + s$

$\implies \: 50 = 30 + s$

$\implies \: s \: = 50 - 30$

$\implies \: s \: = 20cm$

• All 3 sides of given ∆ are 15,15,20cm.

$area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - b)}$

here ,

• s = semi perimeter
• a,b,c are sides of ∆

$\implies \: s = \frac{15 + 15 + 20}{2}$

$\implies \: s = 25$

• a , b = 15 and c = 20

Area =

$\sqrt{25(25 - 15)(25 - 15)(25 - 20)}$

$\implies \: \sqrt{25 \times 10 \times 10 \times 5}$

$\implies \: 5 \times 10 \times \sqrt{5}$

$\implies \: 50 \sqrt{5} cm^{2}$

Therefore , the area of given triangle is 50√5 sq cm.