Question

The length of a rectangular plot of land is 15m more than its breadth.Find it's area if the perimeter is 70cm.​

Answer 1

Answer:

45,30

Step-by-step explanation:

Let the breadth=x

the length =x+15

given perimeter=150

we know  

Perimeter of rectangle=2(l+b)

150 = 2( x+ x+15)

75=2x+15

60=2x

30=x

therefore breadth =30 cm  

length   =30+15=45 cm

check  

150=2(45+30)

150=2(75)

150=150  

LHS=RHS

hence proved.

Answer 2

Appropriate Question

The length of a rectangular plot of land is 15m more than its breadth. Find it's area if the Perimeter is 70 m.

$\large\underline{\sf{Solution-}}$

Given that,

• The length of a rectangular plot of land is 15m more than its breadth.

Let assume that

• Breadth of rectangle = x m

So,

• Length of rectangle = x + 15 m

Further given that,

Perimeter of rectangle = 70 m

We know,

$\red{\rm :\longmapsto\:\sf{\:Perimeter_{(rectangle)} = 2(Length+Breadth)}}$

On substituting the values, we get

$\rm :\longmapsto\:70 = 2(x + x + 15)$

$\rm :\longmapsto\:35 = 2x + 15$

$\rm :\longmapsto\:35 - 15 = 2x$

$\rm :\longmapsto\:20 = 2x$

$\bf\implies \:x = 10$

So,

$\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{Breadth \: = \: 10 \: m} \\ \\ &\sf{Length \: = \: 25 \: m} \end{cases}\end{gathered}\end{gathered}$

So,

$\red{\rm :\longmapsto\:\sf{\:Area_{(rectangle)} = Length \times Breadth}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Area_{(rectangle)} = 25 \times 10$

$\rm :\longmapsto\:\boxed{\tt{ \: \: \: \: Area_{(rectangle)} = 250 \: {m}^{2} \: \: \: }}$

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$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$