Question 2 of 10intermediate🔧 ApplyNumerical3 marks

Now measure the diagonal of the rectangle. How many centimetres do you get? Using the scale, calculate the real length of the playground's diagonal, in metres.

Correct Answer

The diagonal of a 4 cm × 3 cm rectangle measures 5 cm on the map.

Using the scale 1 cm = 10 m, the actual diagonal length is 5 cm × 10 m/cm = 50 metres.

Exercise: LET'S EXPLORE | Q: 6 | (Page Page 10)
For More Understanding

Explanation

The diagonal of a rectangle can be found using the Pythagorean theorem: diagonal² = length² + width². For a 4 cm × 3 cm rectangle, diagonal = 42+32\sqrt{4² + 3²} = 16+9\sqrt{16 + 9} = 25\sqrt{25} = 5 cm. Using the scale, the real diagonal is 5×105 \times 10 = 50 metres.

Solution Steps

  1. Step 1: The rectangle on map measures 4 cm × 3 cm

  2. Step 2: Using Pythagorean theorem: diagonal = 42+32\sqrt{4² + 3²} = 16+9\sqrt{16 + 9} = 25\sqrt{25} = 5 cm

  3. Step 3: Apply scale: 5 cm × 10 m/cm = 50 metres

  4. Step 4: The real diagonal of the playground is 50 metres

PreviousNext