Question

if a rhombous has a perimeter of 60 cm and one of its diagonals measures 20 cm then the area of the rhombous.​

Answer 1

→ Perimeter of Rhombus = 60cm.

→ So, Each side of Rhombus = (Perimeter/4) = (60/4) = 15cm.

And, Now, we know That, Any Diagonal of a Rhombus Divide it into Two Equal Isosceles ∆ area.

So, Now, we Have :-

→ An Isosceles ∆ with sides , 15cm,15cm & 20cm.

So,

→ Semi-Perimeter of Isosceles ∆ = s = (15 + 15 + 20)/2 = 25cm.

Therefore,

→ Area of Isosceles ∆ with Heron's formula = √[s(s - a)(s - b)(s - c)]

Putting values Now, we get :-

→ Area of Isosceles ∆ = √[25*(25-15)*(25-15)*(25-20)]

→ Area of Isosceles ∆ = √[25 * 10 * 10 * 5]

→ Area of Isosceles ∆ = 10√(5 * 5 * 5)

→ Area of Isosceles ∆ = 10 * 5 * √5

→ Area of Isosceles ∆ = 50√5 cm².

Hence,

→ Area of Rhombus = 2 * Area of Isosceles ∆ = 50√5 * 2 = 100√5 cm². (Ans.)