Question

A business recently upgraded a conference TV they had in their conference room. Originally the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches. The new TV is 46 inches across the diagonal. Since the new TV will be recessed in the wall, it will need trim put on the border. What is the perimeter of the new TV? Round your answer to two decimal places.

Answer 1

To find the perimeter of the new TV, use the concept of similar triangles and set up a proportion to solve for x.

Step-by-step explanation:

To find the perimeter of the new TV, we can use the concept of similar triangles. Since the original TV and the new TV have the same shape, their corresponding sides are proportional. We can set up a proportion to solve for the perimeter of the new TV.

Let x be the perimeter of the new TV. We can set up the following proportion:

(46/32) = (x/87.16)

Cross-multiplying, we get:

46*87.16 = 32*x

Simplifying, we have:

x = (46*87.16)/32

Without the specific dimensions of the original TV, the second step can't be accurately carried out, and therefore, we can't determine the perimeter of the new TV with the given information.

Calculating, we find that the perimeter of the new TV is approximately 125.08 inches.