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:
Length of the square field = 4 m
∴ A {rea of the square field = 4 x 4 = 16 m}² 
Given: Area of the rhombus = Area of the square field
Length of one diagonal of the rhombus = 2 m
∴ Side of the rhombus \[=\frac{1}{2}\sqrt{d_1^2 + d_2^2}\]
And, area of the rhombus \[=\frac{1}{2} \times ( d_1 \times d_2 )\]
∴ Area:
\[16 = \frac{1}{2}(2 \times d_2 )\]
\[ d_2 =16 m\]
Now, we need to find the length of the side of the rhombus.
∴ Side of the rhombus \[=\frac{1}{2}\sqrt{2^2 + {16}^2}=\frac{1}{2}\sqrt{260}=\frac{1}{2}\sqrt{4 \times 65}=\frac{1}{2}\times2\sqrt{65}=\sqrt{65}m\]
Also, we know: Area of the rhombus = Side X Altitude
\[ \therefore 16=\sqrt{65}\times \] Altitude
Altitude \[=\frac{16}{\sqrt{65}}m\]