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

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=(1764)/(337)\to x=\sqrt{(1764)/(337)}`

`\text{The area:}\\\\A_1=16\sqrt{(1764)/(337)}\cdot9\sqrt{(1764)/(337)}=(16)(9)\left(\sqrt{(1764)/(337)}\right)^2\\\\=144\cdot(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=√(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.}`