Question

please say the answer and give full explanation ​

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the Concept of Perimeter of Rectangle has been used. We see that we are given the relation between the Length and Breadth of rectangle. Even we are given the perimeter of rectangle. So firstly, we can apply the length and breadth in equation and find one value. Then from that we can find the dimensions of the rectangle.

Let's do it !!

____________________________________________

★ Formula Used :-

$\\\;\boxed{\sf{\pink{Perimeter\;of\;Rectangle\;=\;\bf{2(Length\;+\;Breadth)}}}}$

____________________________________________

★ Solution :-

Given,

» Length (L) = 25 + Breadth (B)

» Perimeter of Rectangle = 170 m

• Let the breadth of the rectangle be 'B'

• Then, length will be '(25 + B)'

Now using the formula of Perimeter, we get

$\\\;\sf{:\rightarrow\;\;Perimeter\;of\;Rectangle\;=\;\bf{2(Length\;+\;Breadth)}}$

Now by applying values, we get

$\\\;\sf{:\Longrightarrow\;\;170\;=\;\bf{2(L\;+\;B)}}$

$\\\;\sf{:\Longrightarrow\;\;170\;=\;\bf{2((25\;+\;B)\;+\;B)}}$

$\\\;\sf{:\Longrightarrow\;\;170\;=\;\bf{2(25\;+\;B\;+\;B)}}$

$\\\;\sf{:\Longrightarrow\;\;170\;=\;\bf{2(25\;+\;2B)}}$

$\\\;\sf{:\Longrightarrow\;\;170\;=\;\bf{50\;+\;4B}}$

$\\\;\sf{:\Longrightarrow\;\;4B\;=\;\bf{170\;-\;50}}$

$\\\;\sf{:\Longrightarrow\;\;4B\;=\;\bf{120}}$

$\\\;\sf{:\Longrightarrow\;\;B\;=\;\bf{\dfrac{120}{4}}}$

$\\\;\sf{:\Longrightarrow\;\;B\;=\;\bf{\red{30\;\;m}}}$

$\\\;\underline{\boxed{\tt{Breadth\;\;of\;\;Rectangle\;=\;\bf{\blue{30\;\;m}}}}}$

Now, we know that

✒ Length = B + 25 = 30 + 25 = 55 m

$\\\;\underline{\boxed{\tt{Length\;\;of\;\;Rectangle\;=\;\bf{\purple{55\;\;m}}}}}$

____________________________________________

★ Verification :-

~ Case I ::

✒ L = 25 + B

✒ 55 = 25 + 30

✒ 55 = 55

Clearly, LHS = RHS

~ Case II ::

✒ 2(L + B) = 170

✒ 2(55 + 30) = 170

✒ 2(85) = 170

✒ 170 = 170

Clearly LHS = RHS.

Both the conditions are satisfied here.

So, our answer is correct.

Hence, Verified.

___________________________________________

★ More to know :-

$\\\;\sf{\leadsto\;\;Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\sf{\leadsto\;\;Diagonal\;of\;Rectangle\;=\;\sqrt{(Length^{2}\;+\;Breadth^{2})}}$

• Properties of Rectangle ::

• Opposite sides are equal and parallel.

• Sum of adjacent angles = 180°

• All the angles of rectangle = 90°

• Diagonals bisect each other at 90°

Answer 2

Step-by-step explanation:

let , the breadth be x

the length will be x + 25

given that,

perimeter = 170m

ATQ,

x + x+25 = 170m

2x = 170m - 25

x = 145m/2

x = 72.5m

the dimensions are = 72.5 m and 97.5 m