The length of a rectangle is 7 centimeters less than its width. What are the dimensions of the rectangle if its area is 260 square​ centimeters?

Answer 1

Hi Angeliga S

Width is 20

Length is 13

You can set up your parameters then set then equal to the given area according the formula for the area of a Rectangle which is

Area = Length * Width = 260

Let A = Area

Let L = Length

Let W = Width

Given L = W - 7 and area is 260 we have

260 = W(W - 7)

260 = W² - 7W

Next we subtract 260 from both sides of the equation to form a quadratic

0 = W² - 7W - 260

We factor the Quadratic

(W - 20)(W + 13) = 0

Length cannot be negative, so -13, or (W + 13) =0 is not a useful factor

W - 20 = 0, W = 20

L = W - 7 = 20 - 7 = 13

Checking

A = L*W

A = 13*20=260

I hope this helps

Answer 2

Hi!

We know that the length of the rectangle is 7 centimeters less than its width. Let's call the width of the rectangle "W." Since the length is 7 centimeters less than the width, we can represent the length as "W - 7".

Now, we are given that the area of the rectangle is 260 square centimeters. The formula for the area of a rectangle is length multiplied by width. So, we can write the equation:

Area = Length × Width

260 = (W - 7) × W

To solve this equation, we can use the distributive property to expand the equation:

260 = W² - 7W

Now, let's rearrange the equation to make it easier to solve. We want the equation to be in the form of a quadratic equation, which is ax² + bx + c = 0. In this case, we have:

W² - 7W - 260 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula.

Let's factor it:

(W - 20)(W + 13) = 0

This is why we set quadratic equations equal to zero, so we know that at least one of the factors must be zero. We have two possible solutions for W: (W - 20) = 0 or (W + 13) = 0.

Solving for W in the first equation, we get:

W - 20 = 0 W = 20

Solving for W in the second equation, we get:

W + 13 = 0 W = -13

Since we are dealing with the dimensions of a rectangle, the width cannot be negative. Therefore, the only valid solution is W = 20.

So, the width of the rectangle is 20 centimeters. To find the length, we can substitute this value back into the expression we defined earlier:

Length = W - 7

Length = 20 - 7

Length = 13 centimeters

Therefore, the dimensions of the rectangle are 20 centimeters by 13 centimeters.

I hope that helps!