ISEE Lower Level Quantitative : Quadrilaterals

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

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Example Questions

Example Question #1411 : Common Core Math: Grade 4

What is the length of a yard with a perimeter of \(\displaystyle 32ft\) and a width of \(\displaystyle 9ft?\)

 

Possible Answers:

\(\displaystyle 6ft\)

\(\displaystyle 7ft\)

\(\displaystyle 4ft\)

\(\displaystyle 3ft\)

\(\displaystyle 5ft\)

Correct answer:

\(\displaystyle 7ft\)

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. 

\(\displaystyle 32=2l+2(9)\)

\(\displaystyle 32=2l+18\)

Subtract \(\displaystyle 18\) from both sides

\(\displaystyle 32-18=2l+18-18\)

\(\displaystyle 14=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{14}{2}=\frac{2l}{2}\)

\(\displaystyle 7=l\)

Example Question #113 : Solving For Length

What is the length of a yard with a perimeter of \(\displaystyle 30ft\) and a width of \(\displaystyle 10ft?\)

 

Possible Answers:

\(\displaystyle 9ft\)

\(\displaystyle 6ft\)

\(\displaystyle 8ft\)

\(\displaystyle 7ft\)

\(\displaystyle 5ft\)

Correct answer:

\(\displaystyle 5ft\)

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. 

\(\displaystyle 30=2l+2(10)\)

\(\displaystyle 30=2l+20\)

Subtract \(\displaystyle 20\) from both sides

\(\displaystyle 30-20=2l+20-20\)

\(\displaystyle 10=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{10}{2}=\frac{2l}{2}\)

\(\displaystyle 5=l\)

Example Question #5701 : Ssat Elementary Level Quantitative (Math)

What is the length of a yard with a perimeter of \(\displaystyle 34ft\) and a width of \(\displaystyle 8ft?\)

 

Possible Answers:

\(\displaystyle 9ft\)

\(\displaystyle 8ft\)

\(\displaystyle 12ft\)

\(\displaystyle 11ft\)

\(\displaystyle 10ft\)

Correct answer:

\(\displaystyle 9ft\)

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. 

\(\displaystyle 34=2l+2(8)\)

\(\displaystyle 34=2l+16\)

Subtract \(\displaystyle 16\) from both sides

\(\displaystyle 34-16=2l+16-16\)

\(\displaystyle 18=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{18}{2}=\frac{2l}{2}\)

\(\displaystyle 9=l\)

Example Question #5702 : Ssat Elementary Level Quantitative (Math)

What is the length of a yard with a perimeter of \(\displaystyle 18ft\) and a width of \(\displaystyle 4ft?\)

 

Possible Answers:

\(\displaystyle 7ft\)

\(\displaystyle 4ft\)

\(\displaystyle 3ft\)

\(\displaystyle 6ft\)

\(\displaystyle 5ft\)

Correct answer:

\(\displaystyle 5ft\)

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. 

\(\displaystyle 18=2l+2(4)\)

\(\displaystyle 18=2l+8\)

Subtract \(\displaystyle 8\) from both sides

\(\displaystyle 18-8=2l+8-8\)

\(\displaystyle 10=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{10}{2}=\frac{2l}{2}\)

\(\displaystyle 5=l\)

Example Question #471 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

What is the length of a yard with a perimeter of \(\displaystyle 24ft\) and a width of \(\displaystyle 5ft?\)

 

Possible Answers:

\(\displaystyle 7ft\)

\(\displaystyle 8ft\)

\(\displaystyle 4ft\)

\(\displaystyle 5ft\)

\(\displaystyle 6ft\)

Correct answer:

\(\displaystyle 7ft\)

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. 

\(\displaystyle 24=2l+2(5)\)

\(\displaystyle 24=2l+10\)

Subtract \(\displaystyle 10\) from both sides

\(\displaystyle 24-10=2l+10-10\)

\(\displaystyle 14=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{14}{2}=\frac{2l}{2}\)

\(\displaystyle 7=l\)

Example Question #117 : Solving For Length

What is the length of a yard with a perimeter of \(\displaystyle 20ft\) and a width of \(\displaystyle 6ft?\)

 

Possible Answers:

\(\displaystyle 4ft\)

\(\displaystyle 7ft\)

\(\displaystyle 6ft\)

\(\displaystyle 8ft\)

\(\displaystyle 5ft\)

Correct answer:

\(\displaystyle 4ft\)

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. 

\(\displaystyle 20=2l+2(6)\)

\(\displaystyle 20=2l+12\)

Subtract \(\displaystyle 12\) from both sides

\(\displaystyle 20-12=2l+12-12\)

\(\displaystyle 8=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{8}{2}=\frac{2l}{2}\)

\(\displaystyle 4=l\)

Example Question #111 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

What is the length of a yard with a perimeter of \(\displaystyle 14ft\) and a width of \(\displaystyle 5ft?\)

 

Possible Answers:

\(\displaystyle 1ft\)

\(\displaystyle 4ft\)

\(\displaystyle 3ft\)

\(\displaystyle 5ft\)

\(\displaystyle 2ft\)

Correct answer:

\(\displaystyle 2ft\)

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. 

\(\displaystyle 14=2l+2(5)\)

\(\displaystyle 14=2l+10\)

Subtract \(\displaystyle 10\) from both sides

\(\displaystyle 14-10=2l+10-10\)

\(\displaystyle 4=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{4}{2}=\frac{2l}{2}\)

\(\displaystyle 2=l\)

Example Question #119 : Solving For Length

What is the length of a yard with a perimeter of \(\displaystyle 22ft\) and a width of \(\displaystyle 2ft?\)

 

Possible Answers:

\(\displaystyle 5ft\)

\(\displaystyle 9ft\)

\(\displaystyle 6ft\)

\(\displaystyle 8ft\)

\(\displaystyle 7ft\)

Correct answer:

\(\displaystyle 9ft\)

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. 

\(\displaystyle 22=2l+2(2)\)

\(\displaystyle 22=2l+4\)

Subtract \(\displaystyle 4\) from both sides

\(\displaystyle 22-4=2l+4-4\)

\(\displaystyle 18=2l\)

Divide \(\displaystyle 2\) by both sides

\(\displaystyle \frac{18}{2}=\frac{2l}{2}\)

\(\displaystyle 9=l\)

Example Question #241 : Measurement & Data

Angela has a garden that she wants to put a fence around. How much fencing will she need if her garden is \(\displaystyle 6ft\) by \(\displaystyle 3ft?\)

 

Possible Answers:

\(\displaystyle 16ft\)

\(\displaystyle 18ft\)

\(\displaystyle 20ft\)

\(\displaystyle 19ft\)

\(\displaystyle 17ft\)

Correct answer:

\(\displaystyle 18ft\)

Explanation:

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

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

\(\displaystyle P=2(6)+2(3)\)

\(\displaystyle P=12+6\)

\(\displaystyle P=18\)

Example Question #1422 : Common Core Math: Grade 4

Angela has a garden that she wants to put a fence around. How much fencing will she need if her garden is \(\displaystyle 4ft\) by \(\displaystyle 10ft?\)

 

Possible Answers:

\(\displaystyle 27ft\)

\(\displaystyle 29ft\)

\(\displaystyle 25ft\)

\(\displaystyle 26ft\)

\(\displaystyle 28ft\)

Correct answer:

\(\displaystyle 28ft\)

Explanation:

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

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

\(\displaystyle P=2(4)+2(10)\)

\(\displaystyle P=8+20\)

\(\displaystyle P=28\)

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