A rectangular television screen has a diagonal of length 42 inches - Junior Cycle Mathematics - Question 9 - 2015

Since the television screen is rectangular, we can apply Pythagoras' theorem:

$w^2 + l^2 = 42^2$

Substituting for w, we have:

$\left( \frac{16}{9} l \right)^2 + l^2 = 42^2$

This simplifies to:

$\frac{256}{81} l^2 + l^2 = 1764$

Combining the terms:

$\frac{256}{81} l^2 + \frac{81}{81} l^2 = 1764$

This leads to:

$\frac{337}{81} l^2 = 1764$

Multiplying both sides by ( \frac{81}{337} ):

$l^2 = 1764 \times \frac{81}{337}$

Calculating the value gives:

$l^2 = \frac{142884}{337}$

Now, we can find the area using. Area A is given by:

$A = w \times l$

Substituting for w:

$A = l \times \frac{16}{9} l = \frac{16}{9} l^2$

Substituting value for ( l^2 ):

$A = \frac{16}{9} \times \frac{142884}{337}$

Calculating this gives:

$A = 754 \text{ in}^2$

Thus, the area is 754 in² correct to the nearest whole number.