ACT Math - How to find the length of the diagonal of a kite

The long diagonal of a kite measures inches, and cuts the shorter diagonal into two pieces. If one of those pieces measures inches, what is the length in inches of the short diagonal?

Explanation

The long diagonal of a kite always bisects the short diagonal. Therefore, if one side of the bisected diagonal is inches, the entire diagonal is inches. It does not matter how long the long diagonal is.

A kite has two perpendicular interior diagonals. One diagonal has a measurement of and the area of the kite is $6\textup{,}250\textup{ units}^{2}$ . Find the sum of the two perpendicular interior diagonals.

$2\textup{,}000$

Explanation

First find the length of the missing diagonal before you can find the sum of the two perpendicular diagonals.

To find the missing diagonal, apply the area formula:

This question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

$6,250=\frac{250\times diagonal B}{2}$

$6250\times2=250\times diagonalB$

$diagonal B=\frac{12,500}{250}=50$

Therefore, the sum of the two diagonals is:

A kite has two perpendicular interior diagonals. One diagonal has a measurement of and the area of the kite is $54\textup{ units}^{2}$ . Find the length of the other interior diagonal.

Explanation

This problem can be solved by applying the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$54=\frac{9\times diagonal B}{2}$

$54\times2=9\times diagonalB$

$diagonal B=\frac{108}{9}=12$

A kite has two perpendicular interior diagonals. One diagonal has a measurement of $22\textup{mm}$ and the area of the kite is $297\textup{mm}^{2}$ . Find the length of the other interior diagonal.

$27\textup{mm}$

$25\textup{mm}$

$37\textup{mm}$

$35\textup{mm}$

$19\textup{mm}$

Explanation

This problem can be solved by applying the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$297=\frac{22\times diagonal B}{2}$

$297\times2=22\times diagonalB$

$diagonal B=\frac{594}{22}=27$

A kite has two perpendicular interior diagonals. One diagonal has a measurement of and the area of the kite is $45\textup{ units}^{2}$ . Find the length of the other interior diagonal.

Explanation

This problem can be solved by applying the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$45=\frac{18\times diagonal B}{2}$

$45\times2=18\times diagonalB$

$diagonal B=\frac{90}{18}=5$

A kite has two perpendicular interior diagonals. One diagonal has a measurement of and the area of the kite is $51\textup{ units}^{2}$ . Find the sum of the two perpendicular interior diagonals.

Explanation

First find the length of the missing diagonal before you can find the sum of the two perpendicular diagonals.

To find the missing diagonal, apply the area formula:

This question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

$51=\frac{17\times diagonal B}{2}$

$51\times2=17\times diagonalB$

$diagonal B=\frac{102}{17}=6$

Therefore, the sum of the two diagonals is:

A kite has two perpendicular interior diagonals. One diagonal has a measurement of $38\textup{cm}$ and the area of the kite is $855\textup{cm}^{2}$ . Find the length of the other interior diagonal.

$45\textup{cm}$

$48\textup{cm}$

$33\textup{cm}$

$15\textup{cm}$

$22.5\textup{cm}$

Explanation

This problem can be solved by applying the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$855=\frac{38\times diagonal B}{2}$

$855\times2=38\times diagonalB$

$diagonal B=\frac{1,710}{38}=45$

A kite has two perpendicular interior diagonals. One diagonal has a measurement of and the area of the kite is $1\textup{,}800\textup{ units}^{2}$ . Find the sum of the two perpendicular interior diagonals.

$3\textup{,}000$

Explanation

You must find the length of the missing diagonal before you can find the sum of the two perpendicular diagonals.

To find the missing diagonal, apply the area formula:

This question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

$1800=\frac{40\times diagonal B}{2}$

$1800\times2=40\times diagonalB$

$diagonal B=\frac{3,600}{40}=90$

Therefore, the sum of the two diagonals is:

Kite vt act

The area of the kite shown above is $125\textup{ units}^{2}$ and the red diagonal has a length of . Find the length of the black (horizontal) diagonal.

Explanation

To find the length of the black diagonal apply the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$125=\frac{25\times diagonal B}{2}$

$125\times2=25\times diagonalB$

$diagonal B=\frac{250}{25}=10$

A kite has two perpendicular interior diagonals. One diagonal is twice the length of the other diagonal. The total area of the kite is $196\textup{ units}^{2}$ . Find the length of each interior diagonal.

$14\textup{ and }28$

$15\textup{ and }30$

$15\textup{ and }45$

$7^2\textup{ and }15$

$7\textup{ and }14$

Explanation

To solve this problem, apply the formula for finding the area of a kite:

$Area=\frac{diagonalA\times diagonalB}{2}$

However, in this problem the question only provides information regarding the exact area. The lengths of the diagonals are represented as a ratio, where