Question 356831
Jolly builds a large corkboard for her room that is 45 inches tall and 63 inches wide .she wants to build a smaller corkboard with a similar shape for the kitchen. Which of the following could be the dimensions of that corkboard?

A     4 in by  3 in
B     7 in  by  5 in 
C    12 in  by  5 in
D    21 in by  14 in

<pre>
We try each one:

{{{(shorter_side_of_large_corkboard)/(longer_side_of_large_corkboard)}}}{{{""=""}}}{{{(shorter_side_of_small_corkboard)/(longer_side_of _small_corkboard)}}}

Try A

{{{45/63}}}{{{""=""}}}{{{3/4}}}

Cross multiply:

{{{45*4}}}{{{""=""}}}{{{3*63}}}

{{{180}}}{{{""=""}}}{{{189}}}

No that's false, so A isn't the answer.

Try B

{{{45/63}}}{{{""=""}}}{{{5/7}}}

Cross multiply:

{{{45*7}}}{{{""=""}}}{{{5*63}}}

{{{315}}}{{{""=""}}}{{{315}}}

That's true, so B is the correct answer.  But let's go though the
others anyway to show that they are not the correct answer:

Try C

{{{45/63}}}{{{""=""}}}{{{5/12}}}

Cross multiply:

{{{45*12}}}{{{""=""}}}{{{5*63}}}

{{{540}}}{{{""=""}}}{{{315}}}

No that's false, so C isn't the answer.

Try D

{{{45/63}}}{{{""=""}}}{{{14/21}}}

Cross multiply:

{{{45*21}}}{{{""=""}}}{{{14*63}}}

{{{945}}}{{{""=""}}}{{{882}}}

No that's false, so D isn't the answer.

The correct answer is B

Edwin</pre>