 okay so in this question it's given that the perimeter of a triangular field right so triangular field and its perimeter is given and it is given to be equal to 450 meters and its sides are in the ratio of 13 is to 12 is to 5 so first of all we'll have to do data mining so if you see this is the data given what is this 450 meters so hence just let's jot down all the you know given information so perimeter is given and perimeter is 450 meters right what else is given side ratios are in 13 is to 12 is to 5 so let's quickly draw our triangle and you know that this is there are three sides to a triangle and let's say this is a this is b and this is c and their ratio a is to b is to c a is to c is given as 13 is to 12 is to 5 okay so we can as you in such cases the moment there are ratios given so what best you can do is let the sides be let the sides be of length 13 x 12 x and 5 x right so if you see they have the same ratio 13 is to 12 is to 5 that means now what you have to find out area right so for area what do you need to do first let's find out the perimeter so very semi perimeter that is so s is a plus b plus c by 2 okay and but before that perimeter is given and so it's also perimeter by 2 perimeter by 2 so hence it is if you see 450 upon 2 is equal to a plus b plus c upon 2 this implies 450 is equal to a plus b plus c so a is 13 x b is 12 x and c is 5 x so it is nothing but if you see this implies 450 is equal to I have dropped the units here just for the calculation sake so it is 13 plus 12 is 25 plus 5 is 30 x so x clearly is 450 upon 30 which is equal to 15 okay now that we know x we can find out the length of the side so a is or was 13 x so hence it is 13 13 time 13 time 13 time 15 13 times 15 that is equal to 195 and the units were in meter I believe so hence it will be in meters and b was 12 x which is nothing but 12 into 15 which is 180 meters and c will be equal to 5 x so hence it is 5 into 15 which is equal to 75 meter right so as we know what was s s was perimeter by 2 so it is 450 by 2 which is 225 now we are trying to find out the area which was a given objective now s is this much s minus a will be equal to 225 minus 195 and this is nothing but 30 meters so let the units be also there s minus b is 225 minus 180 and if you see this is 25 here and 20 there so 45 meters and and now third is s minus c which is 225 minus 75 is equal to 25 plus 100 125 plus 25 150 meters is it it guys so hence now let's find out the area so area is given as under root s s minus a s minus b and s minus c so which is equal to under root s what is s 225 b ready to factorize guys 30 into 45 into 150 is it this means if you just factorize and then think out square root so 25 is nothing but if you know 15 square so it is very easy so 15 will come out and 30 is actually there is no you know square powers on the factors here the 30 can be written as 2 into 3 into 5 45 can be written as 9 into 5 and 150 can be written as 15 times 10 or 25 times 6 better so it is 5 square into 3 into 5 3 into 2 sorry 3 into 2 this one will be 2 so 3 into 2 6 into 25 right so what all can be brought out of 15 can be brought out from here 115 can come out 1 3 can come out and 1 5 can come out and also if you see there are 2 2's so this 2 and this 2 so 1 2 can also come out similarly this 3 and 5 3 and 5 there are 2 3's and 2 5 so 1 3 and 1 5 will come out so this will be the area of the given triangular field and this happens to be 15 into 3 right so we have 3 into 5 and there are 3 into 5 again so 15 was written as 3 into 5 this is 3 into 5 again into 3 into 5 into 2 oh great so that means it's 3 cube into 5 cube into 2 3 cube into 5 cube into 2 and which is equal to if you do the calculation you'll get 6 7 5 0 meter cube 6 7 5 0 meter cube now places where you'll make mistake clearly here when you do the final calculations so be you know alert be very very conscious and you know of your calculation so this is a fair you know simple arithmetic so hence whenever you are doing calculation you should be very very cautious and always when you find the result you go back and check once again so in in such cases in such questions in exam you put a star mark so that you can always go back and check the calculation this is a calculation intensive problem calculation intensive so hence knowing the formula and applying it would not be difficult but you will tend to lose marks because of wrong calculations okay so please bear that in mind