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ISEE Lower Level Quantitative : Plane Geometry

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

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #462 : Rectangles

What is the length of a yard with a perimeter of 24ft $\displaystyle 24ft$ and a width of 3ft? $\displaystyle 3ft?$

Possible Answers:

10ft $\displaystyle 10ft$

7ft $\displaystyle 7ft$

11ft $\displaystyle 11ft$

8ft $\displaystyle 8ft$

9ft $\displaystyle 9ft$

Correct answer:

9ft $\displaystyle 9ft$

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.

$\displaystyle 24=2l+2(3)$

24=2l+6 $\displaystyle 24=2l+6$

Subtract $\displaystyle 6$ from both sides

$\displaystyle 24-6=2l+6-6$

18=2l $\displaystyle 18=2l$

Divide $\displaystyle 2$ by both sides

$\frac{18}{2}=\frac{2l}{2}$ $\displaystyle \frac{18}{2}=\frac{2l}{2}$

9=l $\displaystyle 9=l$

Report an Error

Example Question #463 : Rectangles

What is the length of a yard with a perimeter of 26ft $\displaystyle 26ft$ and a width of 5ft? $\displaystyle 5ft?$

Possible Answers:

9ft $\displaystyle 9ft$

8ft $\displaystyle 8ft$

6ft $\displaystyle 6ft$

5ft $\displaystyle 5ft$

7ft $\displaystyle 7ft$

Correct answer:

8ft $\displaystyle 8ft$

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.

$\displaystyle 26=2l+2(5)$

$\displaystyle 26=2l+10$

Subtract $\displaystyle 10$ from both sides

$\displaystyle 26-10=2l+10-10$

16=2l $\displaystyle 16=2l$

Divide $\displaystyle 2$ by both sides

$\frac{16}{2}=\frac{2l}{2}$ $\displaystyle \frac{16}{2}=\frac{2l}{2}$

8=l $\displaystyle 8=l$

Report an Error

Example Question #464 : Rectangles

What is the length of a yard with a perimeter of 18ft $\displaystyle 18ft$ and a width of 3ft? $\displaystyle 3ft?$

Possible Answers:

2ft $\displaystyle 2ft$

6ft $\displaystyle 6ft$

4ft $\displaystyle 4ft$

3ft $\displaystyle 3ft$

5ft $\displaystyle 5ft$

Correct answer:

6ft $\displaystyle 6ft$

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.

$\displaystyle 18=2l+2(3)$

18=2l+6 $\displaystyle 18=2l+6$

Subtract $\displaystyle 6$ from both sides

$\displaystyle 18-6=2l+6-6$

12=2l $\displaystyle 12=2l$

Divide $\displaystyle 2$ by both sides

$\frac{12}{2}=\frac{2l}{2}$ $\displaystyle \frac{12}{2}=\frac{2l}{2}$

6=l $\displaystyle 6=l$

Report an Error

Example Question #465 : Rectangles

What is the length of a yard with a perimeter of 30ft $\displaystyle 30ft$ and a width of 8ft? $\displaystyle 8ft?$

Possible Answers:

11ft $\displaystyle 11ft$

8ft $\displaystyle 8ft$

10ft $\displaystyle 10ft$

9ft $\displaystyle 9ft$

7ft $\displaystyle 7ft$

Correct answer:

7ft $\displaystyle 7ft$

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.

$\displaystyle 30=2l+2(8)$

$\displaystyle 30=2l+16$

Subtract $\displaystyle 16$ from both sides

$\displaystyle 30-16=2l+16-16$

14=2l $\displaystyle 14=2l$

Divide $\displaystyle 2$ by both sides

$\frac{14}{2}=\frac{2l}{2}$ $\displaystyle \frac{14}{2}=\frac{2l}{2}$

7=l $\displaystyle 7=l$

Report an Error

Example Question #466 : Rectangles

What is the length of a yard with a perimeter of 36ft $\displaystyle 36ft$ and a width of 8ft? $\displaystyle 8ft?$

Possible Answers:

12ft $\displaystyle 12ft$

13ft $\displaystyle 13ft$

11ft $\displaystyle 11ft$

14ft $\displaystyle 14ft$

10ft $\displaystyle 10ft$

Correct answer:

10ft $\displaystyle 10ft$

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.

$\displaystyle 36=2l+2(8)$

$\displaystyle 36=2l+16$

Subtract $\displaystyle 16$ from both sides

$\displaystyle 36-16=2l+16-16$

20=2l $\displaystyle 20=2l$

Divide $\displaystyle 2$ by both sides

$\frac{20}{2}=\frac{2l}{2}$ $\displaystyle \frac{20}{2}=\frac{2l}{2}$

10=l $\displaystyle 10=l$

Report an Error

Example Question #467 : Rectangles

What is the length of a yard with a perimeter of 28ft $\displaystyle 28ft$ and a width of 5ft? $\displaystyle 5ft?$

Possible Answers:

11ft $\displaystyle 11ft$

9ft $\displaystyle 9ft$

12ft $\displaystyle 12ft$

10ft $\displaystyle 10ft$

8ft $\displaystyle 8ft$

Correct answer:

9ft $\displaystyle 9ft$

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.

$\displaystyle 28=2l+2(5)$

$\displaystyle 28=2l+10$

Subtract $\displaystyle 10$ from both sides

$\displaystyle 28-10=2l+10-10$

18=2l $\displaystyle 18=2l$

Divide $\displaystyle 2$ by both sides

$\frac{18}{2}=\frac{2l}{2}$ $\displaystyle \frac{18}{2}=\frac{2l}{2}$

9=l $\displaystyle 9=l$

Report an Error

Example Question #161 : Quadrilaterals

What is the length of a yard with a perimeter of 12ft $\displaystyle 12ft$ and a width of 2ft? $\displaystyle 2ft?$

Possible Answers:

5ft $\displaystyle 5ft$

3ft $\displaystyle 3ft$

6ft $\displaystyle 6ft$

4ft $\displaystyle 4ft$

2ft $\displaystyle 2ft$

Correct answer:

4ft $\displaystyle 4ft$

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.

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

12=2l+4 $\displaystyle 12=2l+4$

Subtract $\displaystyle 4$ from both sides

$\displaystyle 12-4=2l+4-4$

8=2l $\displaystyle 8=2l$

Divide $\displaystyle 2$ by both sides

$\frac{8}{2}=\frac{2l}{2}$ $\displaystyle \frac{8}{2}=\frac{2l}{2}$

4=l $\displaystyle 4=l$

Report an Error

Example Question #162 : Quadrilaterals

What is the length of a yard with a perimeter of 18ft $\displaystyle 18ft$ and a width of 2ft? $\displaystyle 2ft?$

Possible Answers:

4ft $\displaystyle 4ft$

6ft $\displaystyle 6ft$

5ft $\displaystyle 5ft$

8ft $\displaystyle 8ft$

7ft $\displaystyle 7ft$

Correct answer:

7ft $\displaystyle 7ft$

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.

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

18=2l+4 $\displaystyle 18=2l+4$

Subtract $\displaystyle 4$ from both sides

$\displaystyle 18-4=2l+4-4$

14=2l $\displaystyle 14=2l$

Divide $\displaystyle 2$ by both sides

$\frac{14}{2}=\frac{2l}{2}$ $\displaystyle \frac{14}{2}=\frac{2l}{2}$

7=l $\displaystyle 7=l$

Report an Error

Example Question #163 : Quadrilaterals

What is the length of a yard with a perimeter of 26ft $\displaystyle 26ft$ and a width of 4ft? $\displaystyle 4ft?$

Possible Answers:

9ft $\displaystyle 9ft$

6ft $\displaystyle 6ft$

7ft $\displaystyle 7ft$

8ft $\displaystyle 8ft$

5ft $\displaystyle 5ft$

Correct answer:

9ft $\displaystyle 9ft$

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.

$\displaystyle 26=2l+2(4)$

26=2l+8 $\displaystyle 26=2l+8$

Subtract $\displaystyle 8$ from both sides

$\displaystyle 26-8=2l+8-8$

18=2l $\displaystyle 18=2l$

Divide $\displaystyle 2$ by both sides

$\frac{18}{2}=\frac{2l}{2}$ $\displaystyle \frac{18}{2}=\frac{2l}{2}$

9=l $\displaystyle 9=l$

Report an Error

Example Question #91 : How To Find The Perimeter Of A Rectangle

What is the length of a yard with a perimeter of 16ft $\displaystyle 16ft$ and a width of 11ft? $\displaystyle 11ft?$

Possible Answers:

5ft $\displaystyle 5ft$

4ft $\displaystyle 4ft$

6ft $\displaystyle 6ft$

7ft $\displaystyle 7ft$

8ft $\displaystyle 8ft$

Correct answer:

4ft $\displaystyle 4ft$

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.

$\displaystyle 16=2l+2(4)$

16=2l+8 $\displaystyle 16=2l+8$

Subtract $\displaystyle 8$ from both sides

$\displaystyle 16-8=2l+8-8$

8=2l $\displaystyle 8=2l$

Divide $\displaystyle 2$ by both sides

$\frac{8}{2}=\frac{2l}{2}$ $\displaystyle \frac{8}{2}=\frac{2l}{2}$

4=l $\displaystyle 4=l$

Report an Error

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Plane Geometry

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #462 : Rectangles

Example Question #463 : Rectangles

Example Question #464 : Rectangles

Example Question #465 : Rectangles

Example Question #466 : Rectangles

Example Question #467 : Rectangles

Example Question #161 : Quadrilaterals

Example Question #162 : Quadrilaterals

Example Question #163 : Quadrilaterals

Example Question #91 : How To Find The Perimeter Of A Rectangle

All ISEE Lower Level Quantitative Resources

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