Your school wants to take out an ad in the paper congratulating the basketball team on a successful season, as shown to the right. The area of the photo will be half the area of the entire ad. What is the value of​ x?

length 5 in
width 4 in

To find the value of "x", we need to determine the area of the entire ad and the area of the photo. Then we can set up an equation and solve for "x".

Given:
Length of the ad = 5 inches
Width of the ad = 4 inches

Since the area of a rectangle is given by the formula A = length * width, we can calculate the area of the ad:

Area of the ad = 5 inches * 4 inches = 20 square inches

According to the problem, the area of the photo is half the area of the entire ad. Therefore, the area of the photo is:

Area of the photo = (1/2) * 20 square inches = 10 square inches

Now, let's determine the dimensions of the photo using the given information.

Since the photo is a rectangle, we can assume the length of the photo is 'l' and the width of the photo is 'w'. Therefore, we have:

Length of the photo = l inches
Width of the photo = w inches

We are given that the area of the photo is 10 square inches. Using the formula A = length * width, we can set up the equation:

10 square inches = l inches * w inches

Now, we need to find a pair of factors of 10 that satisfy this equation. The factors of 10 are 1, 2, 5, and 10.

Let's try these factors:

If l = 1 inch and w = 10 inches, then 1 inch * 10 inches = 10 square inches (not equal to 10 square inches).

If l = 2 inches and w = 5 inches, then 2 inches * 5 inches = 10 square inches (matches the desired area).

Therefore, the dimensions of the photo are:

Length of the photo = 2 inches
Width of the photo = 5 inches

According to the question, the width of the entire ad is x inches, which is given as 4 inches. Therefore, we can set up another equation to solve for "x":

Width of the ad = Width of the photo
x inches = 4 inches

Hence, the value of "x" is 4 inches.

To find the area of the entire ad, we need to multiply the length and width:

Area of entire ad = length x width

Given that the length is 5 in and the width is 4 in, we have:

Area of entire ad = 5 in x 4 in = 20 in²

Since the area of the photo will be half the area of the entire ad, we have:

Area of photo = 20 in² / 2 = 10 in²

To find the dimensions of the photo, we need to solve for x.

Since the photo is rectangular, its area can be calculated using the formula:

Area of photo = length of photo x width of photo

Given that the width of the photo is x, we can substitute this value into the equation:

10 in² = 5 in x x

Now, we can solve for x:

10 in² = 5x
x = 10 in² / 5
x = 2 in

The value of x is 2 inches.

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