We read your photo as:

A) Write down the formula of magnification. b) Calculate the actual size of the grasshopper if the magnification is 1 1/2 and the image is 3 cm long.

Biology

ScanSolve AI Answer

Answer

b

2 cm\text{2 cm}

Step-by-step solution

4 steps

Part a

Write down the formula of magnification.

The formula for magnification is:

Magnification=Image sizeActual size\text{Magnification} = \frac{\text{Image size}}{\text{Actual size}}

or

Magnification=Length of drawingActual length of object\text{Magnification} = \frac{\text{Length of drawing}}{\text{Actual length of object}}

Part b

2 cm\text{2 cm}

Calculate the actual size of the grasshopper.

  1. Identify the given values.

    The diagram is one and a half times the real size, so the magnification is 1121\frac{1}{2}.
    The diagram (image) is 3 cm3 \text{ cm} long.

  2. Convert the magnification to an improper fraction.

    112=1×2+12=321\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}

  3. Use the magnification formula to find the actual size.

    Magnification=Image sizeActual size\text{Magnification} = \frac{\text{Image size}}{\text{Actual size}}

    Substitute the known values:

    32=3 cmActual size\frac{3}{2} = \frac{3 \text{ cm}}{\text{Actual size}}

  4. Solve for the Actual size.

    Multiply both sides by "Actual size":

    Actual size×32=3 cm\text{Actual size} \times \frac{3}{2} = 3 \text{ cm}

    Multiply both sides by 23\frac{2}{3}:

    Actual size=3 cm×23\text{Actual size} = 3 \text{ cm} \times \frac{2}{3} Actual size=63 cm\text{Actual size} = \frac{6}{3} \text{ cm} Actual size=2 cm\text{Actual size} = \boxed{\text{2 cm}}
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