Rope pieces of lengths 45 cm, 75 cm and 81 cm have to be cut into same size pieces. What is the smallest piece length possible?​

2025 cm

Step-by-step explanation:

Given the length of pieces - 45 cm, 75 cm and 81 cm

To find the length of the rope we have to find the L.C.M. of 45, 75 and 81 :

3  |  45, 75, 81

    |      

3  |  15, 25, 27

    |

3  |    5, 25, 9

    |

3  |    5, 25, 3

    |

5  |    5, 25, 1

    |

5  |     1, 5, 1

    |

    |      1, 1, 1

L.C.M. = 3 × 3 × 3 × 3 × 5 × 5

= 2025 cm

So, the least length of the rope should be 2025 cm which can be cut into a whole number of pieces of length 45 cm, 75 cm and 81 cm.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.