Question

A field is in the form of a rhombus whose each side 81 m and the altitude is 25 m. Find the side of a square field whose area is equal to that of the rhombus . Find the different in the perimeter

Answer 1

GIVEN :-

side of the rhombus field = 81m

altitude of the rhombus field = 25m

we know that rhombus is also a parallelogram whose side is the base

formula to find the area of a parallelogram = base × height

so we can write,

area of the rhombus field = base × height

= 81 × 25

= 2025m²

ATQ, the area of the square field = area of the rhombus field

therefore area of the square field = 2025m²

we know the formula to find the area of a square, that is side × side or side²

➡ side² = 2025m²

➡ side = √2025

➡ side = 45m

now, both the formulas to find the perimeter of a square and a rhombus is same since they have 4 equal sides.

• perimeter of the rhombus field = 4 × 81 = 324m

• perimeter of the square field = 4 × 45 = 180m

hence, difference between their perimeters = 324 - 180

= 144m FINAL ANSWER

Answer 2

Answer :

Difference between their perimeters =  144m

Step-by-step explanation :

Given that :

Side of the rhombus field = 81m.

Altitude of the rhombus field = 25m.

Remember :

$\textbf{ \underline{\underline{Rhombus is also a parallelogram whose side is the base.}}}$

We know that :

$\bigstar\;\boxed{\bf{{Area\; of\; a\; parallelogram = Base \times height}}}$

Put the values :

= 81 × 25

= 2025m²

As given The area of the square field = Area of the rhombus field.

Hence,

$\bf{ \undeline{\underline{Area\; of\; the\; square\; field = 2025m^2}}}$

We also know that :

$\bigstar\;\boxed{\sf Area\;of\;a\; square = Side \times Side}}$

Put Values :

$\sf \longrightarrow Side^2 = 2025m^2\\\\\sf \longrightarrow Side = \sqrt2025\\\\\sf \longrightarrow Side = 45m$

Now to find :

Perimeter of a square and a rhombus.

So,

Perimeter of the rhombus field:

=> 4 × 81

=> 324m

Perimeter of the square field:

=> 4 × 45

=> 180m

Differnce :

324 - 180 = 144.

Hence,

Difference between their perimeters =  144m.