A rectangular garden has length of x+2 and width of x+1 and an area of 42. find the perimeter of this garden.
Answers
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STEP 1 : FORM THE EQUATION WITH X:
length = x + 2 and width = x + 1
Since we know that area = Length x Width
⇒ (x + 2) ( x + 1) = 42
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STEP 2: SOLVE X:
x² + 3x + 2 = 42
x² + 3x - 40 = 0
(x - 5)(x + 8) = 0
x = 5 or x = -8 (rejected, since length cannot be negative)
so x = 5
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STEP 3: FIND LENGTH AND WIDTH:
Now we know that x = 5, we plugged in the value to find the length and width
Length = x + 2 = 5 + 2 = 7 units
Width = x + 1 = 5 + 1 = 6 units
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STEP 4: FIND PERIMETER:
Perimeter = 2 (Length + Width)
Now we know the length is 7 and width is 6
Perimeter = 2( 7 + 6) = 26 units
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ANSWER: Perimeter = 26 units
Area of rectangle= l×b
42=(x+2)×(x+1)
42=x²+x+2x+2
42=x²+3x+2
0=x²+3x+2-42
0=x²+3x-40
0=x²+8x-5x-40
0+x(x+8)-5(x+8)
0=(x-5)(x+8)
x-5=0⇒x=5
x+8=0⇒x=-8
legth nd breadth can't be negative so x=5
length=x+2=5+2=7
width=x+1=5+1=6
perimeter of rectangle=2(l+b)=2(7+6)=2×13=26
Hope it will help u...
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