A parallelogram has a 7-inch side and a 9-inch side, and the longer diagonal is 14 inches long. Find the length of the other diagonal. Do you need your calculator to do it?

then, (Continuation) Evaluate 72 + 92 + 72 + 92 − 142 − d2, where d is the length of the shorter diagonal.

From your description, you are not dealing with a parallelogram but rather a trapezoid. In a parallelogram, the top is parallel to the bottom, and the two sides are also parallel.

By "d2" do you mean "d squared"? (Online, d^2 = d squared.) Is there supposed to be an equal sign anywhere in your "Continuation"?

Repost your questions in clearer terms.

What is the perimeter of a triangle whose sides measure 15cm, 17cm, and 10cm?

Find the side of a square whose diagonal is 16√2 cm.

To find the length of the other diagonal of the parallelogram, we can use the properties of parallelograms.

In a parallelogram, opposite sides are equal in length and opposite angles are congruent. Additionally, the diagonals of a parallelogram bisect each other.

We are given that one side of the parallelogram is 7 inches and another side is 9 inches. We are also given that the longer diagonal is 14 inches.

Since the diagonals of a parallelogram bisect each other, the longer diagonal is divided into two equal parts by the shorter diagonal. Therefore, each of these parts is half the length of the longer diagonal.

To find the length of the other diagonal, we can use the Pythagorean theorem. Let's denote the length of the shorter diagonal as d.

Using the Pythagorean theorem, we have:

(d/2)^2 + 7^2 = 9^2

Simplifying the equation:

(d^2)/4 + 49 = 81

(d^2)/4 = 32

Multiplying both sides by 4:

d^2 = 128

Taking the square root of both sides:

d ≈ 11.3137 inches

So, the length of the other diagonal (which is equal to twice the length of the shorter diagonal) is approximately 2 * 11.3137 inches ≈ 22.6274 inches.

Now, let's evaluate the given expression:

72 + 92 + 72 + 92 − 142 − d^2

By substituting the value of d as 11.3137:

72 + 92 + 72 + 92 − 142 − (11.3137)^2

Calculating each term:

518 + 518 − 142 − 128

Simplifying:

766 − 142 − 128

766 − 270

496

Therefore, the value of the expression 72 + 92 + 72 + 92 − 142 − d^2, with d as the length of the shorter diagonal, is 496.