Question

The frame of a square picture measures \[10\] inches on each side. If the frame has a thickness of \[\dfrac{3}{8}\] inch, find the measure of each side of the picture ?

Answer 1

Hint: This question is the same as the question where we are given a particular figure of any shape and we have to cut another figure from it of the same shape but of smaller size. So to solve this question, we need to keep in mind that while removing the thickness of the frame from the entire length, we have to remove the same length twice and the picture is bounded from both sides by the same thickness of the frame.

Complete step by step solution :
We are given the length of each side of the frame containing a square picture
Let the length of the frame be denoted as \[l1\]
Then \[l1=10\]inch
We will not change the unit of the length because there is only one unit used in the entire question. So we will continue with it.
Now we are given the thickness of the frame on each side . Let it be denoted by \[l2\].
Then \[l2=\dfrac{3}{8}\]inch
To find the length of the picture on each side , we will subtract the thickness of frame on both sides of the picture from the total length of the frame.
Therefore, measure of each side of the picture \[=\text{ }l1-2l2\]
\[\begin{array}{*{35}{l}}
=\text{ }10-2\left( \dfrac{3}{8} \right) \\
   =10-\dfrac{3}{4} \\
   =\dfrac{\left( 40-3 \right)}{4} \\
   =\dfrac{37}{4} \\
\end{array}\]

Hence the measure of each side of the picture is $\dfrac{37}{4}$ inch.

Note :
We need not convert the unit in S.I. unit because all the units used throughout the question are the same and it is not required to unnecessarily increase the work. Here we are given a square frame but if we are given another shape, then the formula used may differ.