We read your photo as:

A framed photograph has outer dimensions of 64 cm by 40 cm, with a 2.5 cm border. Calculate the area of the frame and the dimensions of the photo.

Mathematics

ScanSolve AI Answer

Step-by-step solution

6 steps

Here are the solutions to your questions.

2.1.1 Calculate the area of the wall that will be covered by the framed photograph (frame and photograph).
The dimensions of the framed photograph are given as length L=64 cmL = 64 \text{ cm} and breadth B=40 cmB = 40 \text{ cm}.

  1. Substitute the given dimensions into the area formula.

    A=L×BA = L \times B A=64 cm×40 cmA = 64 \text{ cm} \times 40 \text{ cm}
  2. Calculate the area.

    A=2560 cm2A = 2560 \text{ cm}^2

    The area of the wall covered by the framed photograph is 2560 cm2\boxed{\text{2560 cm}^2}.

    2.1.2 Determine the dimensions (length and breadth) of the photo that will fit in the photo part of the frame.
    The outer frame has a length of 64 cm64 \text{ cm} and a breadth of 40 cm40 \text{ cm}. The border width around the photo is 2.5 cm2.5 \text{ cm} on all sides.

  3. Calculate the length of the photo.

    Length of photo=Outer length−(2×border width)\text{Length of photo} = \text{Outer length} - (2 \times \text{border width}) Length of photo=64 cm−(2×2.5 cm)\text{Length of photo} = 64 \text{ cm} - (2 \times 2.5 \text{ cm}) Length of photo=64 cm−5 cm\text{Length of photo} = 64 \text{ cm} - 5 \text{ cm} Length of photo=59 cm\text{Length of photo} = 59 \text{ cm}
  4. Calculate the breadth of the photo.

    Breadth of photo=Outer breadth−(2×border width)\text{Breadth of photo} = \text{Outer breadth} - (2 \times \text{border width}) Breadth of photo=40 cm−(2×2.5 cm)\text{Breadth of photo} = 40 \text{ cm} - (2 \times 2.5 \text{ cm}) Breadth of photo=40 cm−5 cm\text{Breadth of photo} = 40 \text{ cm} - 5 \text{ cm} Breadth of photo=35 cm\text{Breadth of photo} = 35 \text{ cm}

    The dimensions of the photo are Length=59 cm,Breadth=35 cm\boxed{\text{Length} = 59 \text{ cm}, \text{Breadth} = 35 \text{ cm}}.

    2.1.3 Determine the area of the frame (excluding the photo area) in cm2^2.
    The total area of the framed photograph is 2560 cm22560 \text{ cm}^2 (from 2.1.1).
    The dimensions of the photo are 59 cm59 \text{ cm} by 35 cm35 \text{ cm} (from 2.1.2).

  5. Calculate the area of the photo.

    Area of photo=Length of photo×Breadth of photo\text{Area of photo} = \text{Length of photo} \times \text{Breadth of photo} Area of photo=59 cm×35 cm\text{Area of photo} = 59 \text{ cm} \times 35 \text{ cm} Area of photo=2065 cm2\text{Area of photo} = 2065 \text{ cm}^2
  6. Calculate the area of the frame by subtracting the photo area from the total area.

    Area of frame=Total area of framed photograph−Area of photo\text{Area of frame} = \text{Total area of framed photograph} - \text{Area of photo} Area of frame=2560 cm2−2065 cm2\text{Area of frame} = 2560 \text{ cm}^2 - 2065 \text{ cm}^2 Area of frame=495 cm2\text{Area of frame} = 495 \text{ cm}^2

    The area of the frame (excluding the photo area) is 495 cm2\boxed{\text{495 cm}^2}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp