Question

i) A rectangular field is \[16\dfrac{1}{2}m\] long and \[12\dfrac{2}{5}m\] wide. Find the perimeter of the field.
ii) Evaluate \[88 - \{ 5 - ( - 48) + ( - 16)\} \]

Answer 1

Hint: Here we have two questions. First question can be solved by using the formula of the perimeter of the rectangle. Using given length and width we can find the perimeter of the field easily. Second question can be solved if you know simple addition and some knowledge about multiplications of signs.

Complete step-by-step answer:
i) We know the dimensions of rectangular field are:
Length \[l = 16\dfrac{1}{2}\;m\]
Breadth \[b = 12\dfrac{2}{5}\;m\]
Perimeter of rectangle is \[ = 2(l + b)\]
But we convert mixed fraction into improper fraction.
 \[16\dfrac{1}{2} = \dfrac{{(16 \times 2) + 1}}{2} = \dfrac{{33}}{2}\] Which is length.
 \[12\dfrac{2}{5} = \dfrac{{(12 \times 5) + 2}}{5} = \dfrac{{62}}{5}\] Which is breadth.
Perimeter \[ = 2(l + b)\]
Substituting length and breadth.
 \[ = 2 \times \left( {\dfrac{{33}}{2} + \dfrac{{62}}{5}} \right)\]
L.C.M. of 2 and 5 is 10. Simplifying we get,
 \[ = 2 \times \left( {\dfrac{{(33 \times 5) + (62 \times 2)}}{{10}}} \right)\]
 \[ = 2 \times \left( {\dfrac{{165 + 124}}{{10}}} \right)\]
 \[ = 2 \times \left( {\dfrac{{289}}{{10}}} \right)\] (Dividing 10 by 2)
 \[ = \dfrac{{289}}{5}\;m\]
We can stop here. We can convert this improper fraction to mixed fraction.
 \[ = 57\dfrac{4}{5}\;m\]
We get this result by dividing 289 by 5. We get the remainder 4. Quotient as 57.
Using \[{\text{quotient}}\dfrac{{{\text{remainder}}}}{{{\text{denominator as it is}}{\text{.}}}}\] this, substituting we get the required result.
Hence the perimeter of the field is \[57\dfrac{4}{5}\;m\] .
So, the correct answer is “ \[57\dfrac{4}{5}\;m\] ”.

II) \[88 - \{ 5 - ( - 48) + ( - 16)\} \]
First we simplify the terms in brackets. We know multiplication of negative term and negative term gives positive term and multiplication of positive term and negative term gives negative term. Using this we get:
 \[ = 88 - \{ 5 + 48 - 16\} \]
 \[ = 88 - \{ 37\} \]
 \[ = 51\]
Thus, \[88 - \{ 5 - ( - 48) + ( - 16)\} = 51\]
So, the correct answer is “51”.

Note: In the first problem they gave the dimensions length and width in mixed fraction. Convert it into proper fractions and then solve. Also note the units of both length and width. Sometimes they can ask the perimeter in mixed fraction, that is why we converted the mixed fraction into proper fraction. Second problem all we did is dimple addition.