Question

the carpet must be exactly 4+√7 yards wide by 5+√7 yards long. the salesman must know the total area of the carpet to be prepared for the contractor. what is the area of the carpet? (recall that the area of a rectangle is the width multiplied by the length.

a. 27 square yards
b. 27+√7 square yards
c. 27+9√7 square yards
d. 29+9√7 square yards

Answer 1

Use the FOIL method. Multiple First then Outside the Inside then Last and then add them up.

\[(4+\sqrt{7})\times(5+\sqrt{7})\]

First = \[4\times5=20\]
Outisde = \[4\times \sqrt{7}=4\sqrt{7}\]

Inside = \[\sqrt{7}\times5=5\sqrt{7}\]
Last = \[\sqrt{7}\times\sqrt{7}=7\]

add them up

\[20+4\sqrt{7}+5\sqrt{7}+7=27+9\sqrt{7}\]