A laptop has a screen size of 13 inches with aspect ratio 5:4. Find the length and width of the screen

Question

Please provide solution step by step , thank you!

Answer 1

thinking of the laptop screen as a rectangle.

the screen size is a 13 inch diagonal, so we have two right triangles

aspect ratio 5:4 means the ratio of the longer leg to the shorter leg of the right triangle is 5:4

so if shorter side is x, then longer side is 1.25x.

using Pythagorean Theorem: x^2 + (1.25x)^2 = 13^2

x^2 + 1.56x^2 = 169

2.56x^2 = 169

x^2 = 66

x = 8.125 (width)

x*1.25 = 10.156 (length)

Answer 2

aspect ratio is width compared to height --> 5w=4h

size is the diagonal

s² = w²+h² = w² +(25/16)w² = 13² = 169

169(16) = 41w² -> w = √(169•16/41) = 13•4/6.4 =8.125

h=5/4w = 10.15625