Question

one of the equal sides of an isosceles triangle is 13 cm and it's perimeter is 50cm .find the area of the triangle

Answer 1

Heya !!



Let unequal side be X .




Perimeter = 50 cm



2 × ( equal side ) + Unequal side = 50 cm



2 × 13 + X = 50 cm.



26 + X = 50



X = 50 - 26


X = 24.



Unequal side ( b ) = X = 24 cm



Equal sides ( a ) = 13 cm .





Area of isosceles triangle = 1/2 × b √4a² - b²




=> 1/2 × 24 × √4 × (13)² - (24)²




=> 1/2 × 24 × √4 × 169 - 576




=> 1 /2 × 24 × √ 676 - 576





=> 1/2 × 24 × √100



=> 1/2 × 24 × 10




=> 240/2



=> 120 cm².

Answer 2

Hey !

Let third side be X .

Perimeter = 50 cm

13 + 13 + third side = 50 cm

26 + X = 50

X = 50 - 26

X = 24.

third side ( b ) = 24 cm

equal sides ( a ) = 13 cm .

Area of isosceles triangle = 1/2 × b √4a² - b²

= 1/2 × 24 × √4 × (13)² - (24)²

= 1/2 × 24 × √4 × 169 - 576

= 1/2 × 24 × √100

= 1/2 × 24 × 10

= 240/2

= 120 cm².


Hence, area of isosceles triangle = 120 cm2.