ISEE Middle Level Quantitative : Squares

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

Example Question #111 : Geometry

David wants to put a fence around his backyard. How much fencing will he need if his backyard is \(\displaystyle 10ft\) by \(\displaystyle 9ft?\)

 

Possible Answers:

\(\displaystyle 34ft\)

\(\displaystyle 35ft\)

\(\displaystyle 38ft\)

\(\displaystyle 36ft\)

\(\displaystyle 37ft\)

Correct answer:

\(\displaystyle 38ft\)

Explanation:

The fence is going around the backyard, so this is a perimeter problem. 

\(\displaystyle P=2l+2w\)

\(\displaystyle P=2(10)+2(9)\)

\(\displaystyle P=20+18\)

\(\displaystyle P=38\)

Example Question #511 : Rectangles

What is the length of a rectangular room with a perimeter of \(\displaystyle 88ft\) and a width of \(\displaystyle 20ft?\)

 

Possible Answers:

\(\displaystyle 24ft\)

\(\displaystyle 21ft\)

\(\displaystyle 23ft\)

\(\displaystyle 20ft\)

\(\displaystyle 22ft\)

Correct answer:

\(\displaystyle 24ft\)

Explanation:

\(\displaystyle P=2l+ 2w\)

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\(\displaystyle 88=2l+2(20)\)

\(\displaystyle 88=2l+40\)

Subtract \(\displaystyle 40\) from both sides

\(\displaystyle 88-40=2l+40-40\)

\(\displaystyle 48=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{48}{2}=\frac{2l}{2}\)

\(\displaystyle 24=l\)

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