Evan bought a small 25" TV for her multimedia classroom. The size of the TV is determined by the length of its diagonal. The area of the TV screen is found 300 in², what is the dimension of small Tv?

Question

This is about pre calculus Systems of nonlinear equations

Answer 1

As the area is 300, lw = 300

As the diagonal is 25, √(l² + w²) = 25

Then, l² + w²= 25², or l² + w²= 625

Thus,

lw = 300

l² + w²= 625

(l + w)² = l² + w² +2lw = 625 + 2 * 300 = 1225

Thus, l + w = 35 (we can ignore the negative root, as l and w must be positive)

Now, we have equations that are easy to solve

lw = 300

l + w = 35

w = 35 - l

l(35 -l) = 300

35l- l² = 300

l² - 35l + 300 = 0

(l - 20)(l - 15)= 0

l= 20 and w = 15, or l = 15 and w = 20. Note that these represent the same pair of values.

If we define the larger dimension first, we get a 20" x15" TV.