Question

The lengh and breadth of a rectangle are (x+4) ,(x-4) respectively and its perimeter is 52cm then it's area is​

Answer 1

Answer:

2[x+4+x-4] = 52

2x = 26

x = 13

Length = 13+4 = 17cm

Breadth= 13-4 = 9cm

Area = 17×9 = 153cm²

Hope it helps ✨✨

Answer 2

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 :-

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

Area of a Rectangle :-

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

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 :-

$:\implies \bf{P = 2(Length + Breadth)} \\ \\ \ :\implies \bf{52 = 2[(x + 4) + (x - 4)]} \\ \\ \ :\implies \bf{52 = 2[x + 4 + x - 4]} \\ \\ \ :\implies \bf{52 = 2[x + \not{4} + x - \not{4}]} \\ \\ \ :\implies \bf{52 = 2[x + x]} \\ \\ \ :\implies \bf{52 = 2[2x]} \\ \\ \ :\implies \bf{52 = 4x} \\ \\ \\ :\implies \bf{\dfrac{52}{4} = x} \\ \\ \\ :\implies \bf{13 = x} \\ \\ \\ \therefore \purple{\bf{x = 13}}$

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 :-

$\:\:\:\:\:\:\:\:\:\:\: :\implies \bf{L = (x + 4)} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: :\implies \bf{L = 13 + 4} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: :\implies \bf{L = 17} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: \therefore \purple{\bf{L = 17}}$

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 :-

$\:\:\:\:\:\:\:\:\:\:\: :\implies \bf{B = (x - 4)} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: :\implies \bf{B = 13 - 4} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: :\implies \bf{B = 9} \\ \\ \\ \:\:\:\:\:\:\:\:\:\:\: \therefore \purple{\bf{B = 9 cm}}$

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 :-

$:\implies \bf{A = length \times breadth} \\ \\ \\ :\implies \bf{A = 17 \times 9} \\ \\ \\ :\implies \bf{A = 153} \\ \\ \\ \therefore \purple{\bf{A = 153 cm^{2}}}$.

Hence the Area of the Rectangle is 153 cm².