DSQ: Calculating the length of the side of a rectangle - GMAT Quantitative

To find the area we need the length and width of the rectangle. We can use II together with I to make an equation for perimeter with only one unknown.

So we need both to solve.

Solve for and then go back to find and then with that you can find the area of the base and you are finished.

When asked to find the width of a rectangle we will need to use both statemests together.

For Statement I) we can use the perimeter formula.

Now, for Statement II) we will use the length of the diagonal along with the Pythagorean Theorem.

From here you can solve the perimeter equation in terms of either l or w. Then you can use substitution into the Pythagorean Theorem to solve for a possible width.

Statement 1:

Recall the formula to find the perimeter of a rectangle. Substitute in the given information and solve.

Statement 2:

Recall the formula for the area of a rectangle. Substitute in the given information and solve.

Each statement alone is sufficient to answer the question.

Statement 1:

Statement 1 is sufficient to answer the question

Statement 2:

Statement 2 is also sufficient to answer the question

The length of one diagonal alone does not prove the parallelogram to be a rectangle, nor do the lengths of the sides.

Suppose we know all of these lengths, though. Since is a parallelogram, if , then .

The sides and diagonal form a triangle with sidelengths 25, 60, and 65. The parallelogram is a rectangle if and only if is a right angle; therefore, we must determine whether the conditions of the Pythagorean Theorem hold:

This is true; is a right angle and is a rectangle.

Therefore, both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.

To find the area we need the length and width of the rectangle. We can use II together with I to make an equation for perimeter with only one unknown.

So we need both to solve.

Solve for and then go back to find and then with that you can find the area of the base and you are finished.

When asked to find the width of a rectangle we will need to use both statemests together.

For Statement I) we can use the perimeter formula.

Now, for Statement II) we will use the length of the diagonal along with the Pythagorean Theorem.

From here you can solve the perimeter equation in terms of either l or w. Then you can use substitution into the Pythagorean Theorem to solve for a possible width.

Statement 1:

Recall the formula to find the perimeter of a rectangle. Substitute in the given information and solve.

Statement 2:

Recall the formula for the area of a rectangle. Substitute in the given information and solve.

Each statement alone is sufficient to answer the question.

Statement 1:

Statement 1 is sufficient to answer the question

Statement 2:

Statement 2 is also sufficient to answer the question

The length of one diagonal alone does not prove the parallelogram to be a rectangle, nor do the lengths of the sides.

Suppose we know all of these lengths, though. Since is a parallelogram, if , then .

The sides and diagonal form a triangle with sidelengths 25, 60, and 65. The parallelogram is a rectangle if and only if is a right angle; therefore, we must determine whether the conditions of the Pythagorean Theorem hold:

This is true; is a right angle and is a rectangle.

Therefore, both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.

To find the area we need the length and width of the rectangle. We can use II together with I to make an equation for perimeter with only one unknown.

So we need both to solve.

Solve for and then go back to find and then with that you can find the area of the base and you are finished.

When asked to find the width of a rectangle we will need to use both statemests together.

For Statement I) we can use the perimeter formula.

Now, for Statement II) we will use the length of the diagonal along with the Pythagorean Theorem.

From here you can solve the perimeter equation in terms of either l or w. Then you can use substitution into the Pythagorean Theorem to solve for a possible width.

Statement 1:

Recall the formula to find the perimeter of a rectangle. Substitute in the given information and solve.

Statement 2:

Recall the formula for the area of a rectangle. Substitute in the given information and solve.

Each statement alone is sufficient to answer the question.

Statement 1:

Statement 1 is sufficient to answer the question

Statement 2:

Statement 2 is also sufficient to answer the question

The length of one diagonal alone does not prove the parallelogram to be a rectangle, nor do the lengths of the sides.

Suppose we know all of these lengths, though. Since is a parallelogram, if , then .

The sides and diagonal form a triangle with sidelengths 25, 60, and 65. The parallelogram is a rectangle if and only if is a right angle; therefore, we must determine whether the conditions of the Pythagorean Theorem hold:

This is true; is a right angle and is a rectangle.

Therefore, both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.

To find the area we need the length and width of the rectangle. We can use II together with I to make an equation for perimeter with only one unknown.

So we need both to solve.

Solve for and then go back to find and then with that you can find the area of the base and you are finished.

When asked to find the width of a rectangle we will need to use both statemests together.

For Statement I) we can use the perimeter formula.

Now, for Statement II) we will use the length of the diagonal along with the Pythagorean Theorem.

From here you can solve the perimeter equation in terms of either l or w. Then you can use substitution into the Pythagorean Theorem to solve for a possible width.

Statement 1:

Recall the formula to find the perimeter of a rectangle. Substitute in the given information and solve.

Statement 2:

Recall the formula for the area of a rectangle. Substitute in the given information and solve.

Each statement alone is sufficient to answer the question.

Statement 1:

Statement 1 is sufficient to answer the question

Statement 2:

Statement 2 is also sufficient to answer the question