Question

A field is in the form of a rhombus having its side 81m and altitude 25m. What is the side of a square field which has the same area as that of the rhombus

Answer 1

given :-

side of the Rhombus = 81m

altitude of the Rhombus = 25m

since rhombus is also a parallelogram, we can use height × base formula to find it's area. where height and the base is altitude and side of the Rhombus respectively.

area of the Rhombus = 25 × 81

= 2025m²

ATQ, area of rhombus = area of square

therefore side² is also = 2025m² (since the formula to find square's area is side²)

➡ side² = 2025m²

➡ side = √2025

➡ side = √(45 × 45)

➡ side = 45m

hence, the side of the square is 45m.