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# 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? - Mathematics

Course
ConceptArea of a Polygon

#### 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?

#### Solution

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 $=\frac{16}{\sqrt{65}}m$
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Mathematics for Class 8 by R D Sharma (2019-2020 Session) (2017 to Current)
Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)
Ex. 20.1 | Q: 15 | Page no. 14
Solution 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? Concept: Area of a Polygon.
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