### All SAT Math Resources

## Example Questions

### Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

What is the length of the diagonal of a rectangle that is 3 feet long and 4 feet wide?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

The length and width of a rectangle are in the ratio of 3:4. If the rectangle has an area of 108 square centimeters, what is the length of the diagonal?

**Possible Answers:**

24 centimeters

9 centimeters

15 centimeters

12 centimeters

18 centimeters

**Correct answer:**

15 centimeters

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.

x^{2} = 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*:

length^{2} + width^{2} = c^{2}

9^{2} + 12^{2 }= *c*^{2}

81 + 144 = c^{2}

225 = c^{2}

*c *= 15 centimeters

### Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle whose sides are 8 and 15.

**Possible Answers:**

**Correct answer:**

To solve. simply use the Pythagorean Theorem where and .

Thus,

### Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

The above figure depicts a cube, each edge of which has length 18. Give the length of the shortest path from Point A to Point B that lies completely along the surface of the cube.

**Possible Answers:**

**Correct answer:**

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:

.

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