How to find the length of the diagonal of a rectangle - SAT Math

The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3_x_ and 4_x_.

We also know the area, so we write an equation and solve for x:

(3_x_)(4_x_) = 12_x_2 = 108.

x2 = 9

x = 3

Now we can recalculate the length and the width:

length = 3x = 3(3) = 9 centimeters

width = 4x = 4(3) = 12 centimeters

Using the Pythagorean Theorem we can find the diagonal, c:

length2 + width2 = c2

92 + 122 = _c_2

81 + 144 = c2

225 = c2

c = 15 centimeters

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:

Therefore the diagonal of the rectangle is 5 feet.

To solve. simply use the Pythagorean Theorem where and .

Thus,

The shortest path is along two of the surfaces of the prism. There are three possible choices - top and front, right and front, and rear and bottom - but as it turns out, since all faces are (congruent) squares, all three paths have the same length. One such path is shown below, with the relevant faces folded out:

The length of the path can be seen to be equal to that of the diagonal of a rectangle with length and width 18 and 36, so its length can be found by applying the Pythagorean Theorem. Substituting 18 and 36 for and :

Applying the Product of Radicals Rule:

.

The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3_x_ and 4_x_.

We also know the area, so we write an equation and solve for x:

(3_x_)(4_x_) = 12_x_2 = 108.

x2 = 9

x = 3

Now we can recalculate the length and the width:

length = 3x = 3(3) = 9 centimeters

width = 4x = 4(3) = 12 centimeters

Using the Pythagorean Theorem we can find the diagonal, c:

length2 + width2 = c2

92 + 122 = _c_2

81 + 144 = c2

225 = c2

c = 15 centimeters

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:

Therefore the diagonal of the rectangle is 5 feet.

To solve. simply use the Pythagorean Theorem where and .

Thus,

The shortest path is along two of the surfaces of the prism. There are three possible choices - top and front, right and front, and rear and bottom - but as it turns out, since all faces are (congruent) squares, all three paths have the same length. One such path is shown below, with the relevant faces folded out:

The length of the path can be seen to be equal to that of the diagonal of a rectangle with length and width 18 and 36, so its length can be found by applying the Pythagorean Theorem. Substituting 18 and 36 for and :

Applying the Product of Radicals Rule:

.

The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3_x_ and 4_x_.

We also know the area, so we write an equation and solve for x:

(3_x_)(4_x_) = 12_x_2 = 108.

x2 = 9

x = 3

Now we can recalculate the length and the width:

length = 3x = 3(3) = 9 centimeters

width = 4x = 4(3) = 12 centimeters

Using the Pythagorean Theorem we can find the diagonal, c:

length2 + width2 = c2

92 + 122 = _c_2

81 + 144 = c2

225 = c2

c = 15 centimeters

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:

Therefore the diagonal of the rectangle is 5 feet.

To solve. simply use the Pythagorean Theorem where and .

Thus,

The shortest path is along two of the surfaces of the prism. There are three possible choices - top and front, right and front, and rear and bottom - but as it turns out, since all faces are (congruent) squares, all three paths have the same length. One such path is shown below, with the relevant faces folded out:

The length of the path can be seen to be equal to that of the diagonal of a rectangle with length and width 18 and 36, so its length can be found by applying the Pythagorean Theorem. Substituting 18 and 36 for and :

Applying the Product of Radicals Rule:

.

The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3_x_ and 4_x_.

We also know the area, so we write an equation and solve for x:

(3_x_)(4_x_) = 12_x_2 = 108.

x2 = 9

x = 3

Now we can recalculate the length and the width:

length = 3x = 3(3) = 9 centimeters

width = 4x = 4(3) = 12 centimeters

Using the Pythagorean Theorem we can find the diagonal, c:

length2 + width2 = c2

92 + 122 = _c_2

81 + 144 = c2

225 = c2

c = 15 centimeters

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:

Therefore the diagonal of the rectangle is 5 feet.

To solve. simply use the Pythagorean Theorem where and .

Thus,

The shortest path is along two of the surfaces of the prism. There are three possible choices - top and front, right and front, and rear and bottom - but as it turns out, since all faces are (congruent) squares, all three paths have the same length. One such path is shown below, with the relevant faces folded out:

The length of the path can be seen to be equal to that of the diagonal of a rectangle with length and width 18 and 36, so its length can be found by applying the Pythagorean Theorem. Substituting 18 and 36 for and :

Applying the Product of Radicals Rule:

.

The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3_x_ and 4_x_.

We also know the area, so we write an equation and solve for x:

(3_x_)(4_x_) = 12_x_2 = 108.

x2 = 9

x = 3

Now we can recalculate the length and the width:

length = 3x = 3(3) = 9 centimeters

width = 4x = 4(3) = 12 centimeters

Using the Pythagorean Theorem we can find the diagonal, c:

length2 + width2 = c2

92 + 122 = _c_2

81 + 144 = c2

225 = c2

c = 15 centimeters

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:

Therefore the diagonal of the rectangle is 5 feet.

To solve. simply use the Pythagorean Theorem where and .

Thus,

The shortest path is along two of the surfaces of the prism. There are three possible choices - top and front, right and front, and rear and bottom - but as it turns out, since all faces are (congruent) squares, all three paths have the same length. One such path is shown below, with the relevant faces folded out:

The length of the path can be seen to be equal to that of the diagonal of a rectangle with length and width 18 and 36, so its length can be found by applying the Pythagorean Theorem. Substituting 18 and 36 for and :

Applying the Product of Radicals Rule:

.