Question

if the length of a rectangle is twice is breadth and its area is 162 sqem. Then the perimeter of the red
54 cm
56 cm
50 cm
60 cm​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

GiveN:

• The length is twice the breadth of a rectangle.
• Area of the rectangle = 162 cm²

To FinD:

• Perimeter of the rectangle?

Step-by-Step Explanation:

Let the length and breadth be l and b.

According to question,

⇒ Length = 2(Breadth)

⇒ l = 2b --------(1)

Now we know how to find the area of the rectangle. Area of the rectangle can be calculated by Length × Breadth,

⇒ Length × Breadth = 162 cm²

⇒ l × b = 162 cm²

⇒ 2b × b = 162 cm². (From 1)

⇒ b² = 81 cm²

⇒ b = $\pm$9 cm

But lengths and breadth can't be negative. Hence, b = 9 cm. Then, l = 18 cm.

Finding Perimeter,

⇒ P = 2(l + b)

⇒ P = 2(18 + 9) cm

⇒ P = 2(27) cm

⇒ P = 54 cm

Hence,

The perimeter of the rectangle is:

$\huge{ \boxed{ \sf{ \blue{54 \: cm \: (A)}}}}$

Answer 2

Answer:

$\huge \bf \: given$

Area of rectangle - 162² cm

$\huge \bf \: to \: find$

Perimeter

$\huge \bf \: solution$

Let the breadth be b

Now,

$breadth \: \: = b$

$length \: = 2b$

Now we know that area of rectangle = l × b

$l \: \times b \: = {162 \: cm}^{2}$

$2b \: \times b \: = {162 \: cm}^{2}$

${b}^{2} = {81 \: cm}^{2}$

$b \: = 9 \: cm$

Breadth = 9 cm

Length = 9 × 2 = 18 cm

Verification

$l \: \times b = {162 \: cm}^{2}$

$18 \times 9 = {162 \: cm}^{2}$

$162 =162$

LHS= RHS

Now,

Finding perimeter

As we know that perimeter of rectangle = 2(L+B)

$perimeter \: = 2(18 + 9)$

$perimeter \: = 2 \times 27$

$perimeter \: = 54 \: cm$

Hence Correct option (A)