Question

Find the perimeter of rectangle whose area is 10x^2-9x-7​

Answer 1

Answer :

14x-12

Solution :

Given

Area of rectangle

= 10x² - 9x - 7

= 10x² - 14x + 5x - 7

= 2x(5x - 7) + (5x - 7)

= (5x - 7)(2x + 1)

Also ,

Area of rectangle

= L1×L2

Where L1 and L2 are the dimensions of the rectangle .

Consider L1 = 5x - 7 and L2 = 2x + 1

Now ,

We know that ,

Perimeter of rectangle

= 2(L1 + L2)

•°• P = 2(5x - 7 + 2x + 1)

= 2(7x - 6)

= 14x - 12

Some other approaches

Note :

• Approach one is based on the fact that given in the question , that to find the perimeter of rectangle whose area is 10x²-9x-7
• Approach one , requires the mastery in concept on integrals and finding the area using integration
• Approach 2 is based on assumptions
• I've added a link at the end to make sure that you understand more about the sum and product of roots of a quadratic equation

Solution : (Approach-1)

• Given curve , 10x²-9x-7
• Given that area of rectangle is same as the area of cure , i.e area of curve => area bounded by the curve
• Area bounded by a quadratic curve is given by , Area = ∆^3/2 / 6a²
• ∆ = b²-4ac
• ∆ = (-9)²-4(10)(-7)
• ∆ = 81 + 280
• ∆ = 361
• Area = ∆^3/2 / 6a²
• Area = (361)^3/2 / 6(10)²
• Area = 19³/600
• Area of rectangle = 6859/600
• Area of rectangle = 11.4316.....
• Area of rectangle is 11.43 sq units
• We need some more data, like either length or breadth to find perimeter of rectangle
• So , perimeter becomes unpredictable

Solution : (Approach-2)

If the Question is like , Find the area and perimeter of rectangle if length and breadth are roots of the equation 10x²-9x-7 ?

• Assuming the roots of the given equation as length and breadth ,
• equation = 10x²-9x-7
• Sum of roots = length + breadth ( since we assume that roots are length and breadth) is -b/a
• Sum of roots = -(-9)/10
• l + b = 9/10
• Perimeter = 2(l+b) = 2(9/10) = 18/10 = 1.8 units
• Area = lb = c/a = -7/10 (this is contradiction) Area can never be negative z since one of the root of given eqn is positive and other is negative , we get , negative area , but in real , negative area does not exist

For information regarding the proofs related to sum of roots product of roots of quadratic equation , refer the following question answered by me

https://brainly.in/question/21061855

Answer 2

Answer:

14x-12

Step-by-step explanation:

Question:  Find the perimeter of rectangle whose area is 10x²-9x-7​.

Given : A Rectangle of Area 10x²-9x-7​.

To Find: The perimeter of the Rectangle.

Concept: The Area and perimeter of a Rectangle.

Explanation:-

We L and B be the two sides of the Rectangle.

We know that area of a rectangle is of the form L×B, therefore we'll first

factorise the equation 10x²-9x-7​ =0

10x²-9x-7​=0

⇒ 10x²+5x-14x-7=0

⇒5x(2x+1)-7(2x+1)=0

⇒ (5x-7)(2x+1) =0

Now this is of the form L×B

Let L= (5X-7)

    B = (2x+1)

Now we know That the Perimeter of a Rectangle is of the form 2(L+B)

= 2[ (5x-7)+ (2x+1) ]

= 2[ 7x-6 ]

= 14x-12 (answer)

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