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Activity Discussion Math perimeter of the rectangle

• # perimeter of the rectangle

Posted by on February 16, 2024 at 6:12 pm

The length of a rectangle is 3 more inches than its breadth. The area of the rectangle is 40 in2. What is the perimeter of the rectangle?

replied 1 month, 2 weeks ago 2 Members · 1 Reply
• ### Bharti

Member
February 24, 2024 at 5:30 pm
0

Let’s assume the breadth of the rectangle is x inches.

According to the given information, the length of the rectangle is 3 more inches than its breadth, so the length would be (x + 3) inches.

The area of a rectangle is given by the formula: Area = Length Ã— Breadth.

Plugging in the values we have, we can set up the equation:
40 = (x + 3) Ã— x

Expanding the equation:
40 = x^2 + 3x

Rearranging the equation into a quadratic form:
x^2 + 3x – 40 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring gives us:
(x + 8)(x – 5) = 0

Setting each factor to zero:
x + 8 = 0 or x – 5 = 0

Solving these equations gives us:
x = -8 or x = 5

Since the breadth cannot be negative, we discard the solution x = -8.

Therefore, the breadth of the rectangle is x = 5 inches, and the length is x + 3 = 5 + 3 = 8 inches.

The perimeter of a rectangle is given by the formula: Perimeter = 2 Ã— (Length + Breadth).

Plugging in the values we have:
Perimeter = 2 Ã— (8 + 5) = 2 Ã— 13 = 26 inches.

So, the perimeter of the rectangle is 26 inches.

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