Question

(☝️☝️the question)
The perimeter of an isosceles triangle is 42cm and it's base is 5/2 times each of the equal sides find the length of each side of the triangle, area of the triangle and the height of the triangle.
(please it's urgent)​

Answer 1

Ans. Let the two equal sides be x

Base = (3x/2)

Perimeter of triangle= sum of all sides

42 cm = x+x+(3x/2)

42 cm = (2x+2x+3x)/2

42×2 = 7x

(42×2)/7 = x

12 cm = x

1st side = 2nd side = 12 cm

Base = 3rd side = 3/2×12 = 18 cm

Area of Isosceles triangle ABC =

By Heron's Formula,

a=b= 12cm ,c= 18 cm

Perimeter = 42 cm

Semiperimeter (s)= 42/2 cm = 21 cm

s-a = 21-12= 9 cm

s-b = 21-12= 9 cm

s-c = 21-18= 3 cm

Area of Isosceles ∆ =

√s(s-a)(s-b)(s-c) = √21×9×9×3

= 27√7 cm^2

Height of Isosceles ∆ =

1/2×base×height = Area of triangle

1/2 × 18 × height = 27√7 cm^2

Height of the ∆ = 27√7÷ 9

= 3√7 cm