Question

A rectangular portrait has an area of 40 square feet it's perimeter is 26 feet what are the dimensions of the portrait?

Answer 1

Explanation:

Portrait is in the shape of a rectangle.

And the area of a rectangle = Length × Width

Let the length of the portrait = l

And width of the portrait = w

Area of the portrait = lw

lw = 40

l =
`(40)/(w)`

Perimeter of a rectangle = 2(Length + width)

Perimeter of the portrait = 2(l + w)

26 = 2(l + w)

l + w = 13 ----------(2)

By substituting the value of 'l' in equation (1) from equation (2)

`(40)/(w)+w=13`

40 + w² = 13w

w² - 13w + 40 = 0

w² - 8w - 5w + 40 = 0

w(w - 8) - 5(w - 8) = 0

(w - 5)(w - 8) = 0

w = 5, 8 feet

From equation (2)

l = 8, 5 feet

Therefore, dimensions of the portrait are (5 feet by 8 feet) Or (8 feet by 5 feet).