Question

the length and breadth of a rectangle are x+4 cm and x-4 cm respectively and it's perimeter is 52 cm then what is it's area​

Answer 1

Step-by-step explanation:

To Find :-

The Area of the Rectangle.

Given :-

Length = (x + 4) cm

Breadth = (x - 4) cm

Perimeter = 52 cm

We Know :-

Perimeter of a Rectangle :-

\boxed{\underline{\bf{P = 2(Length + Breadth)}}}P=2(Length+Breadth)

Area of a Rectangle :-

\boxed{\underline{\bf{A = length \times Breadth}}}A=length×Breadth

Concept :-

To Find the Area of the Rectangle first we have to find the length and breadth of the Rectangle.

By the given given perimeter, length (x + 4) and the breadth (x - 4) ,we can find the value of x.

Then substitute it in the length and breadth to get the original length and breadth of the Rectangle.

Solution :-

To Find the value of x :-

Given :-

Length = (x + 4) cm

Breadth = (x - 4) cm

Perimeter = 52 cm

Using the formula for Perimeter of a Rectangle and substituting the values in it , we get :-

\begin{gathered}:\implies \bf{P = 2(Length + Breadth)} \\ \\ \ :\implies \bf{52 = 2[(x + 4) + (x - 4)]} \\ \\ \ :\implies \bf{52 = 2[x + 4 + x - 4]} \\ \\ \ :\implies \bf{52 = 2[x + \not{4} + x - \not{4}]} \\ \\ \ :\implies \bf{52 = 2[x + x]} \\ \\ \ :\implies \bf{52 = 2[2x]} \\ \\ \ :\implies \bf{52 = 4x} \\ \\ \\ :\implies \bf{\dfrac{52}{4} = x} \\ \\ \\ :\implies \bf{13 = x} \\ \\ \\ \therefore \purple{\bf{x = 13}}\end{gathered}:⟹P=2(Length+Breadth) :⟹52=2[(x+4)+(x−4)] :⟹52=2[x+4+x−4] :⟹52=2[x+4+x−4] :⟹52=2[x+x] :⟹52=2[2x] :⟹52=4x:⟹452=x:⟹13=x∴x=13

Hence the value of x is 13.

To Find the length of the Rectangle :-

Given :-

Length = (x + 4)

Putting the value of x ,i.e, (13) in the length(x + 4) , we get :-

\begin{gathered}\:\:\:\:\:\:\:\:\:\:\: :\implies \bf{L = (x + 4)} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: :\implies \bf{L = 13 + 4} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: :\implies \bf{L = 17} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: \therefore \purple{\bf{L = 17}}\end{gathered}:⟹L=(x+4):⟹L=13+4:⟹L=17∴L=17

Hence the length of the Rectangle is 17 cm.

To Find the Breadth of the Rectangle :-

Given :-

Breadth = (x - 4)

Putting the value of x i.e (13) in the breadth(x - 4) , we get :-

\begin{gathered}\:\:\:\:\:\:\:\:\:\:\: :\implies \bf{B = (x - 4)} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: :\implies \bf{B = 13 - 4} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: :\implies \bf{B = 9} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: \therefore \purple{\bf{B = 9 cm}}\end{gathered}:⟹B=(x−4):⟹B=13−4:⟹B=9∴B=9cm

Hence the breadth of the Rectangle is 9 cm.

Area of the Rectangle :-

Length = 17 cm

Breadth = 9 cm

Using the formula for Area of a Rectangle and substituting the values in it , we get :-

\begin{gathered}:\implies \bf{A = length \times breadth} \\ \\ \\ :\implies \bf{A = 17 \times 9} \\ \\ \\ :\implies \bf{A = 153} \\ \\ \\ \therefore \purple{\bf{A = 153 cm^{2}}}\end{gathered}:⟹A=length×breadth:⟹A=17×9:⟹A=153∴A=153cm2 .

Hence the Area of the Rectangle is 153 cm².

Answer 2

Answer:

perimeter of rectangle =2(l+b)

perimeter of rectangle= (x+4+x-4)

=2x

: 52=2x

:x=13

length = x+4=13+4=17

breadth =x-4=13-4=9

area of rectangle =l×b=17×9=153sq.cm