Question

8. A field is in the form of a rhombus whose each side is 81 m and altitude is 25 m.
Find the side of a square field whose area is equal to that of the rhombus. Find the
difference in their perimeters.
T.
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Answer 1

Answer:

hello mate

I hope it helps you

Answer 2

Answer:

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎The side of the square field is 45 m and the difference between the perimeters of two fields is 144 m.

Explanation:

${\underline{\underline{\bf{Given:}}}}$

• The area of rhombus field is equal to the area of square field.
• Side of the rhombus-shaped field = 81 m.
• Height of the rhombus field = 25 m.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

1. The side of the square field.
2. The difference in the perimeters of rhombus-shaped and square fields.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{[Rhombus]}=bh\:sq.units}}}$

$\underline{\boxed{\sf{{Area}_{[Square]}=s^2\:sq.units}}}$

$\underline{\boxed{\sf{{Perimeter}_{[Rhombus]}=4s\:units}}}$

$\underline{\boxed{\sf{{Perimeter}_{[Square]}=4s\:units}}}$

$\:\:\:\:\:\:\:\:\:\:\sf{\bullet\:b\rightarrow base\:(side)}$

$\:\:\:\:\:\:\:\:\:\:\sf{\bullet\:h\rightarrow height}$

$\:\:\:\:\:\:\:\:\:\:\sf{\bullet\:s\rightarrow side}$

${\underline{\underline{\bf{Solution:}}}}$

1) SIDE of the square field:

As we know,

$\rightarrowtail$ Area (Rhombus) = Area (Square)

We can find the side of the square by inserting the given measures in the equation:

$\rightarrowtail{\sf{bh=s^2}}$

$\:\:\:\:\:\:\:\:\implies{\sf{81\times 25=s^2}}$

$\:\:\:\:\:\:\:\:\implies{\sf{2025=s^2}}$

$\:\:\:\:\:\:\:\:\implies{\sf{\sqrt{2025}=s}}$

$\:\:\:\:\:\:\:\:\implies{\underline{\underline{\frak{\red{45\:m=side}}}}}$

2) DIFFERENCE between their perimeters:

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎To find the difference, first we've to find the perimeters of both the fields.

Rhombus-shaped field:-

By applying the formula,

$\leadsto{\sf{4s\:units}}$

$\:\:\:\:\:\implies{\sf{4\times 81}}$

$\:\:\:\:\:\implies\underline{\bf{324\:m}}$

Square field:-

Again, by applying the formula,

$\leadsto{\sf{4s\:units}}$

$\:\:\:\:\:\implies{\sf{4\times 45}}$

$\:\:\:\:\:\implies\underline{\bf{180\:m}}$

$\orange\star$ Difference:-

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{324-180}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\underline{\underline{\frak{\red{144}}}}}$

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