The height of the cover of a speaker cabinet exceeds twice its width by 10 cm. If the area of the cover is 2100 cm , find its dimensions.

Question

Must use quadratic formula 

Answer 1

Height minus two times width equals ten centimeters.

h_____−_____2___×___w____=___10.

Compress to h − 2w = 10.

Height times width equals 2100.

h_____×_____w____=__2100

Compress to hw = 2100. That is, h = 2100/w.

2100/w − 2w = 10. Multiply through (2100/w − 2w = 10) by w

to obtain 2100 − 2w² = 10w.

Rearrange 2100 − 2w² = 10w as 2w² + 10w − 2100 = 0

Divide through [2w² + 10w −2100 = 0] by 2 to gain w² + 5w − 1050 = 0.

For 1w² + 5w − 1050 = 0, calculate w by [-5 ± √(5² − 4×1×-1050)]÷(2×1).

The two solutions compute to 30 and -35.

Discard the negative solution and take width or w as 30 centimeters.

Take height as 2100/30 or 70 centimeters.

Confirm conditions of the problem:

70 cm × 30 cm = 2100 cm².

70 cm − 2 × 30 cm = 10 cm.