How to find the length of the diagonal of a rectangle - GRE Quantitative Reasoning

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

.

We also have that

.

If we then plug this into our equation for perimeter, we get .

Therefore, and . Using the Pythagorean Theorem, we have so .

Suppose ABCD has sides a and b.

The length of one of ABCD's diagonals is given by a2+ b2 = c2, where c is one of the diagonals.

Note that both diagonals are of the same length.

Quantity A: The length of diagonal AC times the length of diagonal BD

This is c * c = c2.

Quantity A = c2 = a2+ b2

Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).

Half of Perimeter = (a + b)

Square Half of Perimeter = (a + b)2

Use FOIL: (a + b)2 = a2+ 2ab + b2

Quantity B = (a + b)2 = a2+ 2ab + b2

The question is asking us to compare a2+ b2 with a2+ 2ab + b2.

Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

.

We also have that

.

If we then plug this into our equation for perimeter, we get .

Therefore, and . Using the Pythagorean Theorem, we have so .

Suppose ABCD has sides a and b.

The length of one of ABCD's diagonals is given by a2+ b2 = c2, where c is one of the diagonals.

Note that both diagonals are of the same length.

Quantity A: The length of diagonal AC times the length of diagonal BD

This is c * c = c2.

Quantity A = c2 = a2+ b2

Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).

Half of Perimeter = (a + b)

Square Half of Perimeter = (a + b)2

Use FOIL: (a + b)2 = a2+ 2ab + b2

Quantity B = (a + b)2 = a2+ 2ab + b2

The question is asking us to compare a2+ b2 with a2+ 2ab + b2.

Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

.

We also have that

.

If we then plug this into our equation for perimeter, we get .

Therefore, and . Using the Pythagorean Theorem, we have so .

Suppose ABCD has sides a and b.

The length of one of ABCD's diagonals is given by a2+ b2 = c2, where c is one of the diagonals.

Note that both diagonals are of the same length.

Quantity A: The length of diagonal AC times the length of diagonal BD

This is c * c = c2.

Quantity A = c2 = a2+ b2

Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).

Half of Perimeter = (a + b)

Square Half of Perimeter = (a + b)2

Use FOIL: (a + b)2 = a2+ 2ab + b2

Quantity B = (a + b)2 = a2+ 2ab + b2

The question is asking us to compare a2+ b2 with a2+ 2ab + b2.

Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

.

We also have that

.

If we then plug this into our equation for perimeter, we get .

Therefore, and . Using the Pythagorean Theorem, we have so .

Suppose ABCD has sides a and b.

The length of one of ABCD's diagonals is given by a2+ b2 = c2, where c is one of the diagonals.

Note that both diagonals are of the same length.

Quantity A: The length of diagonal AC times the length of diagonal BD

This is c * c = c2.

Quantity A = c2 = a2+ b2

Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).

Half of Perimeter = (a + b)

Square Half of Perimeter = (a + b)2

Use FOIL: (a + b)2 = a2+ 2ab + b2

Quantity B = (a + b)2 = a2+ 2ab + b2

The question is asking us to compare a2+ b2 with a2+ 2ab + b2.

Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

.

We also have that

.

If we then plug this into our equation for perimeter, we get .

Therefore, and . Using the Pythagorean Theorem, we have so .

Suppose ABCD has sides a and b.

The length of one of ABCD's diagonals is given by a2+ b2 = c2, where c is one of the diagonals.

Note that both diagonals are of the same length.

Quantity A: The length of diagonal AC times the length of diagonal BD

This is c * c = c2.

Quantity A = c2 = a2+ b2

Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).

Half of Perimeter = (a + b)

Square Half of Perimeter = (a + b)2

Use FOIL: (a + b)2 = a2+ 2ab + b2

Quantity B = (a + b)2 = a2+ 2ab + b2

The question is asking us to compare a2+ b2 with a2+ 2ab + b2.

Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

.

We also have that

.

If we then plug this into our equation for perimeter, we get .

Therefore, and . Using the Pythagorean Theorem, we have so .

Suppose ABCD has sides a and b.

The length of one of ABCD's diagonals is given by a2+ b2 = c2, where c is one of the diagonals.

Note that both diagonals are of the same length.

Quantity A: The length of diagonal AC times the length of diagonal BD

This is c * c = c2.

Quantity A = c2 = a2+ b2

Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).

Half of Perimeter = (a + b)

Square Half of Perimeter = (a + b)2

Use FOIL: (a + b)2 = a2+ 2ab + b2

Quantity B = (a + b)2 = a2+ 2ab + b2

The question is asking us to compare a2+ b2 with a2+ 2ab + b2.

Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

.

We also have that

.

If we then plug this into our equation for perimeter, we get .

Therefore, and . Using the Pythagorean Theorem, we have so .

Suppose ABCD has sides a and b.

The length of one of ABCD's diagonals is given by a2+ b2 = c2, where c is one of the diagonals.

Note that both diagonals are of the same length.

Quantity A: The length of diagonal AC times the length of diagonal BD

This is c * c = c2.

Quantity A = c2 = a2+ b2

Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).

Half of Perimeter = (a + b)

Square Half of Perimeter = (a + b)2

Use FOIL: (a + b)2 = a2+ 2ab + b2

Quantity B = (a + b)2 = a2+ 2ab + b2

The question is asking us to compare a2+ b2 with a2+ 2ab + b2.

Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.

Lets call our longer side L and our shorter side W.

If the perimeter is equal to 68, then

.

We also have that

.

If we then plug this into our equation for perimeter, we get .

Therefore, and . Using the Pythagorean Theorem, we have so .