1. If the sides of a square are lengthened by 7cm, the area becomes 256cm^2. Find the length of a side of the original square.

2. What does it mean to refer to a 20in TV set or a 25in TV set? Such units refer to the diagonal of the screen. A 35 in TV set also has a width of 28inches What is its height.

original side = s

(s+7)^2 = 256
s+7 = 16
s = 9
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use your good old Pythagorean Theorem:

28^2 + h^2 = 35^2
Note that 28=4*7 and 35=5*7, so what we have here is a 3-4-5 triangle scaled up by 7.
h = 3*7 = 21
(check: 28^2 + 21^2 = 784+441 = 1225 = 35^2)

1. To find the length of a side of the original square, we can set up an equation using the given information.

Let's assume the length of a side of the original square is x cm.

According to the problem, if the sides of the square are lengthened by 7 cm, the new length of each side becomes (x + 7) cm.

The area of a square is calculated by squaring the length of one side. Therefore, the area of the square with side length (x + 7) cm is (x + 7)^2 cm^2.

Given that the area of the square is 256 cm^2, we can set up the equation:

(x + 7)^2 = 256

We can solve this equation to find the value of x.

Taking the square root of both sides, we get:

x + 7 = √256
x + 7 = 16

Subtracting 7 from both sides, we get:

x = 16 - 7
x = 9

Therefore, the length of a side of the original square is 9 cm.

2. When referring to a TV set's size, such as a 20in or 25in TV set, these units refer to the diagonal of the screen. The diagonal is the measurement from one corner of the screen to the opposite corner. It represents the length of a line drawn across the screen, connecting the two corners.

For example, a 20in TV set means that the diagonal measurement of the TV screen is 20 inches. Similarly, a 25in TV set means that the diagonal measurement of the TV screen is 25 inches.

Now, let's consider the second part of your question:
A 35 in TV set also has a width of 28 inches. What is its height?

To find the height of the TV set, we can use the concept of right triangles and apply the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal of the screen in this case) is equal to the sum of the squares of the other two sides (the height and the width of the TV set).

Given that the width of the TV set is 28 inches and the diagonal is 35 inches, we can set up the equation:

35^2 = 28^2 + height^2

Simplifying the equation:

1225 = 784 + height^2

Subtracting 784 from both sides:

height^2 = 441

Taking the square root of both sides, we get:

height = √441
height = 21

Therefore, the height of the 35in TV set is 21 inches.