Question

A rectangle has a perimeter of 24m and an area of 35 m2. If the length and width are each increased by 1m, what will be the area of the new rectangle

Answer 1

Answer: 48 square meters

Step-by-step explanation:

Sure, here are the calculations with all numbers presented in plain text:

Let's denote the length of the original rectangle as "l" meters and the width as "w" meters.

Given:

1. Perimeter of the original rectangle = 24 meters.

  Perimeter Equation: 2l + 2w = 24

2. Area of the original rectangle = 35 square meters.

  Area Equation: lw = 35

We have the following equations based on the given conditions:

1. 2l + 2w = 24 (Perimeter equation)

2. lw = 35 (Area equation)

From the perimeter equation, we can express one variable in terms of the other:

l = 12 - w

Substitute l = 12 - w into the area equation:

(12 - w)w = 35

12w - w^2 = 35

w^2 - 12w + 35 = 0

Now we need to solve this quadratic equation. We can use factoring or the quadratic formula to find the values of w.

Factoring:

(w - 5)(w - 7) = 0

This gives us two possible values for w:

1. w = 5

2. w = 7

If w = 5, then l = 12 - 5 = 7.

If w = 7, then l = 12 - 7 = 5.

So, the original dimensions of the rectangle could be l = 7 meters and w = 5 meters, or l = 5 meters and w = 7 meters.

Now, let's find the new dimensions of the rectangle when each dimension is increased by 1 meter:

For the first case: l = 7 meters and w = 5 meters,

New length l_new = 7 + 1 = 8 meters

New width w_new = 5 + 1 = 6 meters

For the second case: l = 5 meters and w = 7 meters,

New length l_new = 5 + 1 = 6 meters

New width w_new = 7 + 1 = 8 meters

The areas of the new rectangles will be:

1. For l_new = 8 meters and w_new = 6 meters: A_new = l_new * w_new = 8 * 6 = 48 square meters.

2. For l_new = 6 meters and w_new = 8 meters: A_new = l_new * w_new = 6 * 8 = 48 square meters.

So, regardless of which set of original dimensions we choose, the area of the new rectangle will be 48 square meters.

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Answer 2

Answer:

48m²

Step-by-step explanation:

The area = 35m² and the perimeter = 24m

This means that the length and width must multiply to get 35 and adding double the width and double the length (to get the perimeter) must = 24

The factor pairs of 35 are 1, 35 and 7, 5

(1 x 2) + (35 x 2) doesn't equal 24 so the length and width must be 7 and 35

Adding 1 to both the length and width we get that the new pair of lengths are 8 and 6.

To find the new area, multiply the new length by the new width (8 x 6) to get 48m²