The sides of a square with an area of 49 cm2 will be reduced by a scale factor of 5/8.
Determine the area of the reduced square to the nearest square centimetre.
Side of square :
a = sqrt ( 49 ) = 7 cm
Side of new square :
a1 = 7 * 5 / 8 = 35 / 8 = 4.375 cm
Area of new square :
A1 = ( 35 / 8 ) ^ 2 = 1225 / 64 = 4.375 ^ 2 = 19,140625 cm ^ 2
To find the area of the reduced square, we first need to determine the length of its sides.
Since the square has an area of 49 cm^2, we can find the length of its sides by taking the square root of the area.
√(49 cm^2) = 7 cm
Next, we will reduce the length of the sides by a scale factor of 5/8.
New side length = (5/8) * 7 cm
New side length = (5 * 7) / 8 cm
New side length = 35 / 8 cm
Finally, we can calculate the area of the reduced square by squaring the new side length.
Area of the reduced square = (35/8 cm)^2
Area of the reduced square ≈ 15 cm^2 (rounded to the nearest square centimeter)
To determine the area of the reduced square, we need to find the length of its side first.
Given that the original square has an area of 49 cm², we can find the length of its side by taking the square root of the area. So, the length of the side of the original square is √49 = 7 cm.
Next, we need to reduce the length of the side by a scale factor of 5/8. To do this, we multiply the length of the side by the scale factor:
Reduced side length = (5/8) * 7 cm = 35/8 cm.
Finally, to find the area of the reduced square, we square this reduced side length:
Area of the reduced square = (35/8 cm)².
To find this value to the nearest square centimeter, we need to calculate the actual value:
Area of the reduced square = (35/8)² = 1225/64 cm².
Now, to round this to the nearest square centimeter, we consider that 1 cm² can be split into 64 equal parts, and we want to find the nearest number of parts to represent the area of the reduced square.
After dividing 1225 cm² by 64 cm², we find that the area of the reduced square is approximately 19.14 cm².
Rounding this to the nearest square centimeter, we get the final answer:
The area of the reduced square is approximately 19 cm².