Question

The perimeter of a rectangle is 49.6 cm, and its diagonal length is 20 cm. Find its length and width.

Answer 1

To find the length and width of a rectangle, we can use the given information about the perimeter and diagonal length.

Step-by-step explanation:

To find the length and width of the rectangle, we can use the given information about the perimeter and diagonal length.

Let's assume the length of the rectangle is L and the width is W.

From the perimeter formula, we know that 2L + 2W = 49.6.

The diagonal of a rectangle forms a right triangle with the length and width as its legs. We can use the Pythagorean theorem to write an equation: L^2 + W^2 = 20^2.

By solving these two equations simultaneously, we can find the values of L and W.

Answer 2

The length of the rectangle is approximately 6.8 cm and the width is approximately 18 cm.

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we can write:

diagonal^2 = length^2 + width^2

We are given that the diagonal length is 20 cm. Substituting this value:

20^2 = length^2 + width^2

400 = length^2 + width^2

The perimeter of a rectangle is the sum of the lengths of all its sides. We are given that the perimeter is 49.6 cm. Let's denote the length as l and the width as w:

perimeter = 2(l + w)

49.6 = 2(l + w)

24.8 = l + w

Now we have two equations with two unknowns:

400 = l^2 + w^2

24.8 = l + w

We can solve for l and w using substitution or elimination. Here, let's use substitution:

From equation 2, express w in terms of l: w = 24.8 - l.

Substitute this expression for w in equation 1: 400 = l^2 + (24.8 - l)^2.

Expand and solve for l: This will give you a quadratic equation. Solve it using the quadratic formula or factoring to get l ≈ 6.8.

Finally, substitute l ≈ 6.8 back into equation 2 to find w ≈ 18.