Question

the length of a rectangle is 3 times its width if the perimeter is 96 cm find the dimensions of the rectangle. find Area

Answer 1

Given:-

• Length of rectangle = 3(Width of the rectangle)
• Perimeter of rectangle = 96 cm

To find:-

• Dimensions of the rectangle (length and breadth)
• Area of rectangle

Answer:-

Let the breadth of the rectangle be x cm.

As it is given that,

Length of rectangle = 3(Width of the rectangle)

=> length = 3(x) cm

=> length = 3x cm

As it is given that,

Perimeter of rectangle = 96 cm

We know that, perimeter of rectangle = 2(length + breadth)

=> 96 = 2(3x + x)

=> 2(4x) = 96

=> 8x = 96

=> x = 12

So,

• breadth = x cm = 12 cm Ans
• length = 3x cm = (3 * 12) cm = 36 cm Ans

We know that,

Area of rectangle = l * b

So,

=> Area of rectangle = 36 cm * 12 cm

=> Area of rectangle = 432 cm² Ans

Answer 2

Answer:

Given :-

• The length of a rectangle is 3 times it's width if the perimeter is 96 cm.

To Find :-

• What is the dimension or length and breadth and its area.

Formula Used :-

To find area of a rectangle we know that,

★ Area of rectangle = Length × Breadth ★

Solution :-

Let, the breadth be x

And, the length be 3x

According to the question,

⇒ 2(3x + x) = 96

⇒ 6x + 2x = 96

⇒ 8x = 96

⇒ x = 96/8

➠ x = 12

Hence, the required dimensions or length and breadth are,

✧ Breadth = x = 12 cm

✧ Length = 3x = 3(12) = 36 cm

∴ The dimensions of a rectangle is 12 cm and 36 cm.

Now, we have to find the area of a rectangle,

Given :

• Length = 36 cm
• Breadth = 12 cm

According to the question by using the formula we get,

↦ Area = 36 cm × 12 cm

➦ Area = 432 cm²

∴ The area of a rectangle is 432 cm² .