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12 August, 19:17

LMNP is a rectangle. Find the value of x and the length of each diagonal. LN = 7x+9 and MP=9x-9

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  1. 12 August, 21:11
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    see explanation

    Step-by-step explanation:

    The diagonals of a rectangle are congruent, thus

    MP = LN, substitute values

    9x - 9 = 7x + 9 (subtract 7x from both sides)

    2x - 9 = 9 (add 9 to both sides)

    2x = 18 (divide both sides by 2)

    x = 9

    LN = 7x + 9 = (7 * 9) + 9 = 63 + 9 = 72

    MP = 9x - 9 = (9 * 9) - 9 = 81 - 9 = 72
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