Question

a rectangular garden has an area of 300 square metres and perimeter of 80 metres.
What
are the length and breadth of the garden
(a) 30 m, 10 m
(b) 25 m, 15 m
(c) 35 m, 5 m
(d) 40 m, 10 m​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• Area of rectangular garden = 300 sq. m

• Perimeter of rectangular garden = 80 m

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• The length and breadth of garden

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the length be "l"

• Let the breadth be "b"

$\:\:$

$\underline{\bold{\texttt{Area of rectangle :}}}$

$\:\:$

$\purple\longrightarrow$ $\bf l \times b$

$\:\:$

$\sf \longmapsto l \times b = 300$ --------(1)

$\:\:$

$\underline{\bold{\texttt{Perimeter of rectangle :}}}$

$\:\:$

$\purple\longrightarrow$ $\bf 2(l + b)$

$\:\:$

$\sf \longmapsto 80 = 2(l + b)$

$\:\:$

$\sf \longmapsto 40 = l + b$

$\:\:$

$\sf \longmapsto l = 40 - b$ ---------(2)

$\:\:$

$\underline{\bold{\texttt{Putting the value of l from (2) to (1) }}}$

$\:\:$

$\sf \longmapsto (40 - b)\times b = 300$

$\:\:$

$\sf \longmapsto 40b - b ^2 = 300$

$\:\:$

$\sf \longmapsto b ^2 - 40b + 300 = 0$

$\:\:$

$\sf \longmapsto b ^2 - 10b - 30b + 300 = 0$

$\:\:$

$\sf \longmapsto b(b - 10) -30(b - 10) = 0$

$\:\:$

$\sf \longmapsto (b - 10)(b - 30) = 0$

$\:\:$

$\sf \longmapsto b = 10 \ or \ b = 30$

$\:\:$

If b = 10m

$\:\:$

$\sf \longmapsto l \times 10 = 300$

$\:\:$

$\bf \longmapsto l = 30m$

$\:\:$

If b = 30m

$\:\:$

$\sf \longmapsto l \times 30 = 300$

$\:\:$

$\bf \longmapsto l = 10m$

$\:\:$

• So , Length and breadth will be 30m and 10m respectively or 10m and 30m respectively.

$\:\:$

So option (i) is correct

Answer 2

$\huge{\underbrace{\sf{\red{^{♡}Answer:}}}}$

$\large{\boxed{\sf{\orange{Option\:(a)\:30m,10m}}}}$

$\huge{\underbrace{\sf{\purple{^{♡}Explanation:}}}}$

Given :

• Area of rectangular garden = 300m²
• Perimeter of the rectangular garden = 80m

To Find:

• Length and breadth.

Solution :

Perimeter of rectangle: $\large{\boxed{\sf{\pink{2(length+breadth)}}}}$

:$\implies{\sf{2(l+b)=80m}}$

:$\implies{\sf{(l+b)= \dfrac{80m}{2}}}$

:$\implies{\sf{(l+b)= 40m}}$

:$\implies{\sf{l= 40m - b}}$

Area of rectangle: $\large{\boxed{\sf{\pink{length \times breadth}}}}$

:$\implies{\sf{l \times b=300m}}$

Putting the value l = 40m - b, we get

:$\implies{\sf{40-b\times b=300m}}$

:$\implies{\sf{40b-b^{2}=300m}}$

:$\implies{\sf{40b-b^{2}+300=0}}$

:$\implies{\sf{b^{2}-40b+300=0}}$

:$\implies{\sf{b^{2}-10b-30b+300=0}}$

:$\implies{\sf{b(-b-10)-30(b-10)=0}}$

:$\implies{\sf{(b-30)(b-10)=0}}$

Hence, b can 30 and 10.

If b = 30

:$\implies{\sf{l \times b=300m}}$

:$\implies{\sf{l \times 30=300m}}$

:$\implies{\sf{l =10m}}$

If b = 10

:$\implies{\sf{l \times b=300m}}$

:$\implies{\sf{l \times 10=300m}}$

:$\implies{\sf{l =30m}}$

Hence, If b = 30 then l = 10 and if b= 10 and l=30.

Therefore the answer is (a) 10,30.

$\rule{400}4$