The length of a side of square field is 4m What will be the altitude of the rhombus if - Maths - Mensuration

Question

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

Aakash Sharma · Accepted Answer

Given : Area of rhombus = Area of square of side 4 cm $\Rightarrow \frac{1}{2} \times ACXBD = (4 m)^{2} \Rightarrow \frac{1}{2} \times AC × 2 {m = 16m}^{2} \Rightarrow AC = 16 m$ Now we know that diagonals of a rhombus are perpendicular bisector of each other $\Rightarrow AO = \frac{1}{2} AC = \frac{1}{2} \times 16 m = 8 m and OB = \frac{1}{2} BD = \frac{1}{2} \times 2 m= 1m$ Now in right Î”AOB AO2 + BO2 = AB2 â‡’AB2 = (8 m)2 + (l m)2 = 64 m2 + 1m2 = 65m2 $\Rightarrow Side of rhombus = AB= \sqrt{65} m$ Let DX be the altitude â‡’AB Ã— DX = Area of rhombus $= \sqrt{65} {m × DX = 16 m}^{2}$ $\Rightarrow DX = \frac{16}{\sqrt{65}} m$

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