Question

Calculate the perimeter of a rectangle whose area is x2 – 25x + 156.​

Answer 1

Answer:The perimeter is 50

Step-by-step explanation:

x^2-25x+156=0

x^2-13x-12x+156=0

x(x-13)-12(x-13)=0

(x-12)(x-13)=0

x-12=0 or x-13=0

x=0+12 or x=0+13

x=12 or x=13

P=2(l+w)

P=2(13+12)

P=2(25)

P=50

Answer 2

Given:

rectangle whose area is x2 – 25x + 156.​

To Find:

Find the perimeter of the rectangle

Solution:

We are given a rectangle with an area in quadratic form and we need to find the perimeter of the rectangle for that we will need to convert the area into a multiplication of two factors, which is possible by factorization,

So we will factorize the expression of the area using splitting the midterm,

$Area=x^2-25x+156\\=x^2-12x-13x+156\\=x(x-12)-13(x-12)\\=(x-13)(x-12)$

So we have the area as multiplication of two terms, now we can say that the length and breadth are (x-13) and (x-12)

The perimeter will be,

P=2(l+b)

P=2(x-13+x-12)

P=2(2x-25)

P=4x-50

Hence, the perimeter is (4x-50).