A rectangular piece of wood is 12 centimeters longer than it is wide. A strip 1 centimeter wide is cut off all around. This decr

Question

3 years ago

14

eases the area by 120 square centimeters. What were the original dimensions?

1 answer:

denis-greek [22] · Answer 1 · 2021-11-28T22:08:29+03:00

Answer:

Length 37 cm, width 25 cm.

Step-by-step explanation:

Let the original dimensions be length x and width x - 12 cms.

The new dimensions will be length (x - 2) and width (x - 12 - 2) = x-14 cm.

So , from the areas, we have:

x(x - 12) - (x - 2)(x - 14) = 120

x^2 - 12x - (x^2 - 16x + 28) = 120

-12x + 16x - 28 = 120

4x = 148

x = 37 cms

So the length was 37 cm and the width was 37-12 = 25 cm.