Michele is making a kite based on the pattern below. About how much binding does Michele need to cover the edges of the kite? The figure shows kite O M R E. Diagonals O R and M E intersect at point P. The length of segment M P is five inches. The length of segment P E is five inches. The length of segment O P is nineteen inches. The length of segment P R is four inches.

about 52.1 in.

Step-by-step explanation:

PM=PE=5 inches, PR=4 inches, and OP=19 inches.

Since the figure is a kite, the diagonals ME and OR are perpendicular and form right triangles with their hypotenuses forming the sides of the kite, OM, MR, RE, and EO.

The figure shows the same kite O M R E as in the beginning of the task. Diagonal O R is perpendicular to diagonal M E.

Use the Pythagorean Theorem to calculate the length of OM.

OM=OP2+PM2−−−−−−−−−−√

Substitute 19 for OP and 5 for PM.

OM=192+52−−−−−−−√

=361+25−−−−−−−√

=386−−−√

Therefore, OM=386−−−√ in.

By the definition of a kite, OM≅EO. So, EO is also equal to 386−−−√ inches.

Use the Pythagorean Theorem to calculate the length of MR.

MR=PM2+PR2−−−−−−−−−−√

Substitute 5 for PM and 4 for PR.

MR=52+42−−−−−−√

=25+16−−−−−−√

=41−−√

Therefore, MR=41−−√ in.

By the definition of a kite, MR≅RE. So, RE is also equal to 41−−√ inches.

The figure shows the same kite O M R E as in the beginning of the task. Sides O M and E O are square root of 386 inches long. Sides M R and R E are square root of 41 inches long.

The perimeter of the kite is the sum of the four sides.

Perimeter of OMRE=OM+MR+RE+EO

=386−−−√+41−−√+41−−√+386−−−√

=2386−−−√+241−−√

Use a calculator to approximate.

Perimeter of OMRE≈52.1 in.

So, the perimeter of OMRE is about 52.1 inches.

Therefore, about 52.1 inches of binding are needed to cover the edges of the kite.

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step-by-step explanation: