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From the figure what is the breadth of the rectangle where the perimeter of the total figure is 7034?
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(a) 450
(b) 500
(c) 550
(d) None

Last updated date: 21st Jul 2024
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Hint: Assume the breadth of the rectangle equal to ‘b’. Now, use the property of a rectangle which says that the opposite sides of a rectangle are equal to find the lengths of all the sides. Take the sum of the outer boundary of the figure leaving the side which is common to both the rectangle and the triangle and equate the sum with 7034. Solve for the value of b to get the answer.

Complete step by step answer:
Here we have been provided with the figure drawn below and we are asked to calculate the breadth of the rectangle. Let us assume the breadth of the rectangle as ‘b’.
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Now, we know that the opposite sides of a rectangle are equal so we have two sides of the rectangle as lengths equal to 2013 and the other two sides as breadths b whose value is to be determined.
We know that the perimeter of a figure is defined as the total length of its outer boundary. In the figure we can clearly see that one of the lengths of the rectangle is common with one of the sides of the triangle and they are not the outside boundary of the figure, so that common side will not be included in the expression for the perimeter. Taking the sum of all the outer sides and equating it with 7034 we get,
$\Rightarrow $ 2011 + 2010 + 2013 + 2b = 7034
$\Rightarrow $ 2b = 1000
$\therefore $ b = 500

So, the correct answer is “Option b”.

Note: You must remember the properties of certain special quadrilaterals like parallelogram, square, rectangle, rhombus etc. as they are often used in topics of area and perimeter. Remember the basic definition of perimeter otherwise you may add the two lengths of the rectangle in the expression of the perimeter which will give the value of b negative which will not be possible.