# Intermediate Geometry : How to find the length of the side of a rhombus

## Example Questions

### Example Question #71 : Quadrilaterals

Find the length of a side of a rhombus if it has diagonals possessing the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

### Example Question #21 : How To Find The Length Of The Side Of A Rhombus

Find the length of a side of a rhombus if it has diagonals possessing the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

### Example Question #73 : Quadrilaterals

Find the length of a side of a rhombus if it has diagonals possessing the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

### Example Question #74 : Quadrilaterals

Find the length of a side of a rhombus if it has diagonals possessing the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

### Example Question #21 : How To Find The Length Of The Side Of A Rhombus

Find the length of a side of a rhombus that has diagonal lengths of  and .

Explanation:

Recall that in a rhombus, the diagonals are not only perpendicular to each other, but also bisect one another.

Thus, we can find the lengths of half of each diagonal and use that in the Pythagorean Theorem to find the length of the side of the rhombus.

First, find the lengths of half of each diagonal.

Now, use these half diagonals as the legs of a right triangle that has the side of the rhombus as its hypotenuse.

Plug in the lengths of the half diagonals to find the length of the rhombus.

Make sure to round to  places after the decimal.

### Example Question #22 : How To Find The Length Of The Side Of A Rhombus

A garden is shaped like a rhombus. If the diagonals of the garden are  feet and  feet in length, in feet, what is the length of feet for a side of the garden?

Explanation:

Recall that in a rhombus, the diagonals are not only perpendicular to each other, but also bisect one another.

Thus, we can find the lengths of half of each diagonal and use that in the Pythagorean Theorem to find the length of the side of the rhombus.

First, find the lengths of half of each diagonal.

Now, use these half diagonals as the legs of a right triangle that has the side of the rhombus as its hypotenuse.

Plug in the lengths of the half diagonals to find the length of the rhombus.

Make sure to round to  places after the decimal.

### Example Question #23 : How To Find The Length Of The Side Of A Rhombus

Find the length of a side of a rhombus that has diagonals with lengths of  and .

Explanation:

Recall that in a rhombus, the diagonals are not only perpendicular to each other, but also bisect one another.

Thus, we can find the lengths of half of each diagonal and use that in the Pythagorean Theorem to find the length of the side of the rhombus.

First, find the lengths of half of each diagonal.

Now, use these half diagonals as the legs of a right triangle that has the side of the rhombus as its hypotenuse.

Plug in the lengths of the half diagonals to find the length of the rhombus.

Make sure to round to  places after the decimal.

### Example Question #78 : Quadrilaterals

Find the length of a side of a rhombus that has diagonals with lengths  and

Explanation:

Recall that in a rhombus, the diagonals are not only perpendicular to each other, but also bisect one another.

Thus, we can find the lengths of half of each diagonal and use that in the Pythagorean Theorem to find the length of the side of the rhombus.

First, find the lengths of half of each diagonal.

Now, use these half diagonals as the legs of a right triangle that has the side of the rhombus as its hypotenuse.

Plug in the lengths of the half diagonals to find the length of the rhombus.

Make sure to round to  places after the decimal.

### Example Question #79 : Quadrilaterals

Find the length of a side of a rhombus that has diagonals with lengths of  and .

Explanation:

Recall that in a rhombus, the diagonals are not only perpendicular to each other, but also bisect one another.

Thus, we can find the lengths of half of each diagonal and use that in the Pythagorean Theorem to find the length of the side of the rhombus.

First, find the lengths of half of each diagonal.

Now, use these half diagonals as the legs of a right triangle that has the side of the rhombus as its hypotenuse.

Plug in the lengths of the half diagonals to find the length of the rhombus.

Make sure to round to  places after the decimal.

### Example Question #24 : How To Find The Length Of The Side Of A Rhombus

Find the length of a side of a rhombus that has diagonals with lengths of  and .

Explanation:

Recall that in a rhombus, the diagonals are not only perpendicular to each other, but also bisect one another.

Thus, we can find the lengths of half of each diagonal and use that in the Pythagorean Theorem to find the length of the side of the rhombus.

First, find the lengths of half of each diagonal.

Now, use these half diagonals as the legs of a right triangle that has the side of the rhombus as its hypotenuse.

Plug in the lengths of the half diagonals to find the length of the rhombus.

Make sure to round to  places after the decimal.