Question

The length of a side of a square field is 4 m. What will be the altitude of the rhombus, if the area of the rhombus is equal to the square field and one of its diagonal is 2 m?

Answer 1

Given that,

Length of a side of a square = 4 m

Area of square = side2

Area of square = 4 × 4 = 16 m2

We know that,

Area of square = Area of rhombus

So, Area of rhombus = 16 m2

Area of rhombus = 1/2 × d1 × d2

16 = 1/2 × 2 × d2

16 = d2

∴ the diagonal of rhombus = 16 m

In ΔAOB,

Using Pythagoras theorem:

AB2 = OA2 + OB2

AB2 = 82 + 12

AB2 = 65

AB = √65

Since rhombus is a parallelogram, therefore area of parallelogram = base × altitude

Area of parallelogram = AB × DE

16 = √65 × DE

DE = 16/√65

i.e., Altitude of Rhombus = 16/√65 cm