the perimeter of a rectangle is 38cm and it's area is 84sq.cm if the length of the rectangle is x and the breadth is y ? find x-y
Answers
y = 20cm.. x = 14cm
Step by step solution:
Let the length of rectangle be x cm and the breadth of the rectangle be y cm
the perimeter of a rectangle is 40 cm
Perimeter = 2 (length + breadth)
Petimeter = 2 (x + y) = 40
=> (x + y) = 20
=> y = 20 + x (Eq. 1)
The area is 84cm²
Area = length × breadth
Area = x × y = 84
=> xy = 84 (Eq. 2)
Substituting the value of y from Eq. 1
=> x (20 - x) = 84
=> 20x - x² = 84
=> x² - 20x + 84 = 0
=> x² - 14x - 6x + 84= 0
=> x (x - 14) - 6 (x - 14)
=> (x - 14) (x - 6) = 0
=> x = 14 cm
the perimeter of rectangle is 38cm.
perimeter of rectangle = 2(L+B)
So,
38cm = 2(L+B)
Or, 38÷2= (L+B)
Or, 19= (L+B)
so, (L+B) = 19cm.
we know that,
the length of rectangle = X
And, the breadth of rectangle = Y
So,
L= X and, B = Y.
So, ( X+Y ) = 19cm. ----------------- ( 1 )
the area of rectangle = 84cm².
and, the area of rectangle = L×B
We already know that,
L= X and B = Y
so,
L × B = 84cm².
and then,
X × Y = 84cm².
XY = 84cm².
(X-Y)² = (X+Y)² - 4XY
= (19)² - 4×84
= 361 - 336
= 25
(X-Y)² = 25
Or, ( X- Y)= 5.
so,
(X- Y) = 5cm (ans.)
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