Question

The area of a rectangular television screen is 3456 in^2. The width is 24 inches longer than the height. What is a quadratic equation that represents the area of the screen?

Answer 1

`0=H^2+24H-3456`

Explanation:

Area=height times width

if we represent height with H and width with W, and area with A, then

A=HW

we are given thatn Area=3456 or A=3456 which leads to 3456=HW

Width is 24 longer than height

W=24+H

so we can combine the 2 equations by subsituting 24+H for W to get

3456=H(24+H)

or expanded

`3456=24H+H^2`

which can be rewritten as

`0=H^2+24H-3456`

which is a quadratic equation that can be solved for H and then subsituted back to get W

Answer 2

h² + 24h - 3456 = 0

Explanation:

The formula for the area of a rectangle is

A = width × height = wh

If A = 3456 and w = h + 24,

(h + 24)h = 3456

h² + 24h = 3456 Distributed the h

h² + 24h - 3456 = 0 Subtracted 3456 from each side

A quadratic equation that represents the area of the screen

is h² + 24h - 3456 = 0.