Question

Which television as more viewing area: the 42 inch 16:9 television or the 32 inch 4:3?

Answer 1

Answer: 42 inch 16:9 television

Step-by-step explanation:

The dimensions of 42 inch 16:9 television are:

Width of the television = 36.6 inches

Height of the television = 20.6 inches

Screen Area of the television = 36.6 x 20.6 = 753.96 sq inches

The dimensions of 32 inch 4:3 television are:

Width of the television = 25.6 nches

Height of the television = 19.2 inches

Screen Area of the television = 25.6 x 19.2 = 491.52 sq inches

Thus 42 inches 16:9 television has 262.44 square inches more screen area.

Hope it helps.

Thanks you :)

Answer 2

$\text{Look at the picture.}$

$x, y - some\ units\ of\ leng th$

$\text{Use the Pythagorean theorem:}$

$(16x)^2+(9x)^2=42^2\\\\256x^2+81x^2=1764\\\\337x^2=1764\qquad\text{divide both sides by 337}\\\\x^2=\dfrac{1764}{337}\to x=\sqrt{\dfrac{1764}{337}}$

$\text{The area:}\\\\A_1=16\sqrt{\dfrac{1764}{337}}\cdot9\sqrt{\dfrac{1764}{337}}=(16)(9)\left(\sqrt{\dfrac{1764}{337}}\right)^2\\\\=144\cdot\dfrac{1764}{337}\approx754\ in^2$

$(4x)^2+(3x)^2=32^2\\\\16x^2+9x^2=1024\\\\25x^2=1024\qquad\text{divide both sides by 25}\\\\x^2=40.96\to x=\sqrt{40.96}\to x=6.4\ in\\\\\text{The area:}\\\\A_2=4(6.4)\cdot3(6.4)=25.6\cdot19.2=491.52\ in^2$

$754 > 491.52$

$\text{Answer: 42 in 16 : 9.}$