Tv questions

Question

The width of a TV screen is 6 inches less than its length. The diagonal is 6 inches more then its length. How many inches is the TV's diagonal?

Answer 1

l² + (l - 6)² = (l + 6)²

l² + l² - 12l + 36 = l² + 12l + 36

l² - 24l = 0

l(l - 24) = 0

 

l = 0. of course not.

 

l - 24 = 0

l = 24

 

24 + 6 = 30

Answer 2

Let W = the width

Let L = the length

Let D = the diagonal

 

The problem states the following:

 

W = L - 6

 

The problem also states the following:

 

D = L + 6

 

From the pythagorean theorem, we also know that:

 

D² = W² + L²

 

Since we have W and D, we can substitute into the 3rd formula to solve for L:

 

(L+6)² = (L-6)² + L²

L² + 12L + 36 = L² - 12L + 36 + L²

12L + 36 = L² - 12L + 36

36 = L² - 24L + 36

0 = L² - 24L

0 = L(L-24)

0 = L - 24

L = 24

 

Since we know that D = L + 6, D = 24 + 6 = 30

Therefore, D = 30