Question

The length, breadth and height of a room are 300cm, 900cm, 1500cm respectively. Find the longest tape which can measure the three dimensions of the room exactlyThe length, breadth and height of a room are 300cm, 900cm, 1500cm respectively. Find the longest tape which can measure the three dimensions of the room exactly

Answer 1

Answer:

Step-by-step explanation:

Length = 825 cm = 3 × 5 × 5 × 11

Breadth = 675 cm = 3 × 3 × 3 × 5 × 5

Height = 450 cm = 2 × 3 × 3 × 5 × 5

Longest tape = HCF of 825, 675, and 450 = 3 × 5 × 5 = 75 cm

Therefore, the longest tape is 75 cm.

lenght = 825 cm = 3×5×5×11

breath = 675 cm =3×3×3×5×5

height = 450 cm = 2×3×3×5×5

longest tape = HCF of 825,675,450 = 3×5×5 = 75 cm

Therefore,longest tape is 75 cm

Answer 2

Answer:

To find the length of the longest tape which can measure the three dimensions of the room, we need to find the H.C.F of length, breadth and height of the room, i.e. , 300 cm , 900 cm, 1500 cms respectively.

Let us factorise all three given dimensions.

825 = 3×5×5×11

675=3×3×3×5×5

450=2×3×3×5×5

Hence, 3, 5 and 5 are the common prime factors here.

So, H.C.F =3×5×5=75

Therefore, we need 75 cm longest tape to measure the three dimensions of the room.