GMAT Math : Calculating the length of the diagonal of a rectangle

Example Questions

Example Question #23 : Rectangles

A rectangle has a length of  and a width of . What is the length of the diagonal of the rectangle?

Explanation:

If the rectangle has a length of  and a width of , we can imagine the diagonal as being the hypotenuse of a right triangle. The length and width are the other two sides to this triangle, so we can use the Pythagorean Theorem to calculate the length of the diagonal of the rectangle:

Example Question #24 : Rectangles

A rectangle has a length of  and a width of . What is the length of the diagonal of the rectangle?

Explanation:

The diagonal of a rectangle can be thought of as the hypotenuse of a right triangle with the length and width of the rectangle as the other two sides. This means we can use the Pythagorean theorem to solve for the diagonal of a rectangle if we are given its length and its width:

Example Question #25 : Rectangles

is a rectangle,  and . What is the length of the diagonal of the rectangle?

Explanation:

Here, we also have a  triangle, indeed both ADC and ABD are   triangles. We can see that by calculating the missing angles. in each triangle we find that this angle to be 30 degrees. Since , we also know that the other sides of the triangles will be  and , since a   triangle have its sides in ratio , where  is a constant. In this case . Therefore the hypotenuse will be , which is also the length of the diagonal of the rectangle.

Example Question #26 : Rectangles

Rectangle  has an area of  and . What is the length of the diagonal ?

Explanation:

Firstly, before we try to set up an equation for the length of the sides and the area, we should notice that the area is a perfect square. Indeed . Now let's try to see whether 13 could be the length of two consecutive sides of the rectangle, Indeed, we are told that , therefore ABDC is a square with side 13 and with diagonal , where  is the length of the side of the square. Therefore, the final answer is .

Example Question #27 : Rectangles

Rectangle , has area  and . What is the length of diagonal ?

Explanation:

To find the length of the sides to calculate the length of the diagonal with the Pythagorean Theorem, we would need to set up two equations for our variables. However, trial and error, in my opinion in most GMAT problems is faster than trying to solve a quadratic equation. The way we should test values for our sides is firstly by finding the different possible factors of the area, that way we can see possible factors.

As follows  has possible factors . From these values we should find the two that will give us 8, the length of the two consecutive sides.

We find that  and  are the values for the two sides.

Now we just need to apply the Pythagorean Theorem to find the length of the diagonal: ,  or .

Example Question #28 : Rectangles

Find the length of the diagonal of a rectangle whose sides are lengths .

Explanation:

To find the diagonal, you must use the pythaorean theorem. Thus:

Example Question #29 : Rectangles

Calculate the length of the diagonal of a rectangle whose width is  and length is .

Explanation:

To solve, simply use the Pythagorean theorem.

Example Question #30 : Rectangles

If a garden bed will have side lengths of 9 meters and 12 meters, what will the distance be across its diagonal?