Question

(a)
The area of a parallelogram and a square are the same. If the perimeter of the
square is 280 m and the height of the parallelogram is 35 m, find the length of
the corresponding base of the parallelogram.​

Answer 1

Answer:

$\bold\red{Base\:of\:parallelogram}$ = $\bold{140\:m}$

Step-by-step explanation:

$\bf\green{Here}\begin{cases}\sf\pink{Area\:of\:square =Area\:of\:parallelogram } \\\sf\red{Perimeter\:of\:square = 280\:m}\\\sf\green{Height\:of\:parallelogram=35\:m}\\\sf\pink{Base\:of\:parallelogram=?}\end{cases}$

$\bigstar{\boxed{\sf\red{Perimeter\:of\:square = 4\times Side }}}$

$\Rightarrow\sf\green{ 280 = 4 \times Side} \\\\\Rightarrow\sf\green {Side = \cancel{\dfrac{280}{4}}\:m} \\\\\Rightarrow{\boxed{\bf\red{Side = 70\:m}}}$

$\bigstar{\boxed{\bf\purple{Area\:of\:square = {(Side)}^{2} }}}$

$\Rightarrow\sf\pink{ Area\:of\:square = {(70)}^{2}} \\\\\Rightarrow{\boxed{\bf\purple{Area\:of\:square = 4900\:{m}^{2} }}}$

$\rule{300}{1}$

$\small{\boxed{\bf\red{Area\:of\:square = Area\:of\:parallelogram}}}$

$\therefore\bf\pink{Area\:of\:parallelogram = 4900\:{m}^{2} }$

$\bigstar{\boxed{\bf\green{Area\:of\:parallelogram = Height \times Base }}}$

$\Rightarrow\sf\red{4900 = 35 \times Base} \\\\\Rightarrow\sf\green{ Base =\cancel{\dfrac{4900}{35} }\:m} \\\\\Rightarrow{\boxed{\bf\pink{Base = 140\:m }}}$

$\therefore\bf\red{Base\:of\:parallelogram = 140\:m }$

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

Given :

• Area of Square = Area of Parallelogram
• Perimeter of square = 250 m
• Height of Parallelogram (H) = 35 m

Solution

Side of Square :

We have formula for Perimeter of square :

$\large \bigstar {\boxed{\sf{Perimeter \: = \: 4 \: \times \: Side}}} \\ \\ \implies {\sf{280 \: = \: 4 \: \times \: Side}} \\ \\ \implies {\sf{Side \: = \: \dfrac{280}{4}}} \\ \\ \implies {\sf{Side \: = \: 70}} \\ \\ \large {\boxed{\sf{Side \: of \: Square \: = \: 70 \: m}}}$

$\rule{200}{1}$

As we know that area of square is :

Area = (Side)² .......(1)

________________________

And are of Parallelogram is :

Area = Base × Height ........(2)

$\rule{200}{2}$

Equate (1) and (2)

$\implies {\sf{(Side)^2 \: = \: Base \: \times \: Height}} \\ \\ \implies {\sf{(70)^2 \: = \: Base \: \times \: 35}} \\ \\ \implies {\sf{4900 \: = \: Base \: \times \: 35}} \\ \\ \implies {\sf{Base \: = \: \dfrac{4900}{35}}} \\ \\ \implies {\sf{Base \: = \: 140}} \\ \\ \large{\boxed{\sf{Base \: is \: of \: 140 \: m}}}$

__________________________

Addition Information :

Square:

• It is a 2-D shape .
• Diagonals are equal .
• All sides and angles are equal.
• Angles are of 90° each.

Parallelogram:

• It is a 2-D shape.
• Diagonals are different.
• Opposite Sides and opposite angles are equal.
• Angles in sides may vary.