Question

the length of a rectangle is 10 cm more than twice its breadth if the perimeter of the recangle is 50 cm find its dimensions and also it's are area​

Answer 1

Step-by-step explanation:

let's the length l = x

and the breath b = y

according to question,

x = 10 + 2y

x-2y = 10________(1)

and,

2(x+y) = 50

x+y = 25__________(2)

from equation 1 & 2,

x = 20cm

y = 5cm

so,

area = l×b

= 20×5

= 100cm² answer

Answer 2

Given :

• Length of rectangle is 10 cm more than twice its breadth.
• Perimeter of rectangle = 50 cm

To Find :

• Length of rectangle = ?
• Breath of rectangle = ?
• Area of rectangle = ?

Solution :

As, we are given that length of rectangle is 10 cm more than twice its breadth.

$\sf : \implies Length = 10 \: cm + 2 \times Breadth$

Let breadth = x

$\sf : \implies Length = 10 \: cm + 2 \times x$

$\sf : \implies Length = 10 \: cm + 2x$

Now, we have perimeter is 50 cm and we know that :

$\large \underline{\boxed{\bf{Perimeter_{(rectangle)} = 2(Length + Breadth)}}}$

By filling values :

$\sf : \implies 50 \: cm= 2(10 \: cm + 2x +x)$

$\sf : \implies 50 \: cm= 2(10 \: cm + 3x)$

$\sf : \implies \cancel{\dfrac{50}{2} }\: cm= 10 \: cm + 3x$

$\sf : \implies 25 \: cm= 10 \: cm + 3x$

$\sf : \implies 25 \: cm - 10 \: cm= 3x$

$\sf : \implies 15 \: cm= 3x$

$\sf : \implies \cancel{\dfrac{15}{3}} \: cm= x$

$\sf : \implies 5 \: cm= x$

$\large \underline{\boxed{\bf{x = 5 \: cm}}}$

Hence,

• Breadth of rectangle = 5 cm
• Length of rectangle = 10 cm + 2 × 5 cm = 10 cm + 10 cm = 20 cm

Now, for area of rectangle, we have a formula :

$\large \underline{\boxed{\bf{Area_{(rectangle)} = Length \times Breadth}}}$

By putting values :

$\sf : \implies Area = 20 \: cm \times 5 \: cm$

$\sf : \implies Area = 100 \: cm^{2}$

$\large \underline{\boxed{\bf{Area = 100 \: cm^{2}}}}$

Hence, Area of rectangle = 100 cm².

So, dimensions of rectangle are 20 cm × 5 cm and Area of rectangle is 100 cm².