# Intermediate Geometry : Kites

## Example Questions

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### Example Question #1 : How To Find If Kites Are Similar

A kite has two different side lengths of  and . Find the measurements for a similar kite.

and

and

and

and

and

and

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides. In order for two kites to be similar their sides must have the same ratios.

Since, the given kite has side lengths  and , they have the ratio of .

Therefore, find the side lengths that have a ratio of .

The only answer choice with this ratio is:

### Example Question #2 : How To Find If Kites Are Similar

A kite has two different side lengths of  and . Find the measurements for a similar kite.

and

and

and

and

and

and

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides. In order for two kites to be similar their sides must have the same ratios.

The given side lengths for the kite are  and , which have the ratio of

The only answer choice with the same relationship between side lengths is:  and , which has the ratio of

### Example Question #3 : How To Find If Kites Are Similar

Suppose the ratio of a kite's side lengths is  to .  Find a similar kite.

Explanation:

To find a similar kite, first take the ratios of the two sides and convert this to fractional form.

Rationalize the denominator.

The ratios of  matches that of .

### Example Question #4 : How To Find If Kites Are Similar

Suppose a kite has side lengths of  and .  What must the side lengths be for a similar kite?

Explanation:

Write the side lengths 4 and 5 as a ratio.

The only side lengths that match this ratio by a scale factor of  is .

Therefore, the correct side lengths are .

### Example Question #1 : How To Find The Perimeter Of Kite

If a kite has lengths of  and , what is the perimeter?

Explanation:

Write the formula to find the perimeter of a kite.

Substitute the lengths and solve.

### Example Question #2 : How To Find The Perimeter Of Kite

If a kite has lengths of  and , what is the perimeter?

Explanation:

Write the formula for the perimeter of a kite.

Substitute the lengths and solve.

### Example Question #3 : How To Find The Perimeter Of Kite

What is the perimeter of a kite if the lengths were  and ?

Explanation:

Write the formula to find the perimeter of a kite.

Substitute the lengths and simplify.

### Example Question #1 : How To Find The Length Of The Side Of A Kite

The diagonals of a kite are  inches and  inches respectively. Two of the sides of the kite are each  inches. Find the length of the other two sides.

Explanation:

We would do best to begin with a picture.

One of our diagonals is bisected by the other, and thus each half is 12.  The other important thing to recall is that the diagonals of a kite are perpendicular.  Therefore we have four right triangles.  We can then use the Pythagorean Theorem to calculate the upper portion of the vertical diagonal to be 5.  That means that the bottom portion of our diagonal is 9.

Using the Pythagorean Theorem, we can calculate our remaining sides to be 15.

### Example Question #2 : How To Find The Length Of The Side Of A Kite

A kite has a perimeter of  inches. One pair of adjacent sides of the kite have a length of  inches. What is the measurement for each of the other two sides of the kite?

Explanation:

To find the missing side of this kite, work backwards using the formula:

, where  and  represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

### Example Question #3 : How To Find The Length Of The Side Of A Kite

A kite has a perimeter of  mm. One pair of adjacent sides of the kite have lengths of  mm. What is the measurement for one of the other two sides of the kite?

Explanation:

To find the missing side of this kite, work backwards using the formula:

, where  and  represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

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