# Perimeter of a rectangle

The perimeter of a rectangle is the sum of the lengths of all of its sides:

P = 2l + 2w

where P is perimeter, l is length, and w is width.

Example:

Find the perimeter of the tennis court with a length of 78 feet and width of 27 feet.

P = | 2l + 2w |

= | 2 × 78 + 2 × 27 |

= | 210 feet |

Example:

Find the perimeter of rectangle whose length is twice the size of its width, and has a diagonal of 10.

The diagonal divides the rectangle into two congruent right triangles. Using the Pythagorean theorem, we can find w:

w^{2} + (2w)^{2} = 10^{2}

w^{2} = 20

w = 2

P = | 2l + 2w |

= | 2(2w) + 2w |

= | 6w |

= | |

= |