Equations
the perimeter of a rectangular plot of land is 120 metres. if the length
s increased by 5 metres and breadth decreased by 5 metres, its area is
decreased by 75 sq. m., find the length and breadth of the plot.

Step-by-step explanation:

Let's define our variables before anything else:

Length = L

Breadth = B

We're going to be setting up two equations:

Our first equation is 2L + 2B = 120, because we know that the length times 2 plus the breadth times two gives the perimeter of a rectangle, which in this case is 120.

Our second equation is (L + 5)(B - 5) = L*B - 75, because we know the original area was length times breadth, and the area was decreased by 75. The new area is the new length (length + 5) times the new breadth (breadth - 5).

Now lets simplify the second equation and plug in one of the values from the top function (it really doesn't matter which, but I chose L):

(L + 5)(B - 5) = L*B - 75

LB - 5L + 5B - 25 = LB - 75

5B - 5L + 50 = 0

2L + 2B = 120

L + B = 60

L = 60 - B

5B - 5(60 - B) + 50 = 0

5B + 5B - 300 + 50 = 0

10B - 250 = 0

10B = 250

B = 25

Great, now we have the breadth of the plot, let's plug that in to whichever function we want to get the length! I'll show multiple examples of different functions we can plug this value into:

2L + 2B = 120

2L + 2(25) = 120

2L + 50 = 120

2L = 70

L = 35

(L + 5)(B - 5) = L*B - 75

(L + 5)(25 - 5) = 25L - 75

(L + 5)(20) = 25L - 75

20L + 100 = 25L - 75

175 = 5L

35 = L

Now we have our two answers! Don't forget your units!

Length = 35 m

Breadth = 25 m

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x