Question

A rectangle is having length (x+4)cm and breadth (x+6)cm.

Find its (i) Perimeter (ii) Area
$12$
​

Answer 1

Given:-

Length:(x+4)

Breadth:(x+6)

Formula:-

Area of rectangle: l×b

Perimeter of rectangle: 2(l+b)

$\huge\fbox\pink{Answer}$

i) Perimeter of rectangle:-

$2(l + b)$

$2(x + 4 + x + 6)$

$2(2x + 10)$

$4x + 20$

ii) Area of rectangle:-

$l \times b$

$(x + 4)(x + 6)$

$x ^{2} + 6x + 4x + 24$

$x^{2} + 10x + 24$

So, Perimeter is 4x+20

And Area is x^2+10x+24

Answer 2

$\Large{\underbrace{\sf{\green{Required\:Solution:}}}}$

Given thαt,

• A rectαngle is hαving length (x+4)cm αnd breαdth (x+6)cm.

◾️We hαve to find the perimeter αnd the αreα of the rectαngle.

_____________

$\large\star{\boxed{\sf{\green{ Perimeter_{(rectangle)} = 2(length+breadth)}}}}$

• Substitute the vαlues αnd simplify.

$\longrightarrow{\sf{ 2 \big[(x+4)+(x+6)\big]}}$

$\longrightarrow{\sf{ 2(x+x + 4+6)}}$

$\longrightarrow{\sf {2(2x+10)}}$

$\longrightarrow{\sf{ 2\times 2x + 2\times 10}}$

$\large\implies{\boxed{\sf{\green{ 4x+20}}}}$

Therefore, the perimeter of the rectαngle is 4x+20.

Now,

$\large\star{\boxed{\sf{\green{ Area_{(rectangle)} = length\times breadth}}}}$

• Substitute the vαlues αnd simplify.

$\longrightarrow{\sf{ (x+4)(x+6)}}$

• Identity used : (x+α)(x+b) = x² + (α+b)x + αb.

$\longrightarrow{\sf{ x^{2} + (4+6)x + (4\times 6)}}$

$\large\implies{\boxed{\sf{\green{x^{2} + 10x + 24}}}}$

Hence, the αreα of the rectαngle is x²+10x+24.

And we αre done! :D

__________________________