Question

Gables property Corp is leasing office buildings with an area of 49x^2 + 70x +25

Explain how to find a possible length and width of the building. What is the possible shape of the building

Answer 1

Given: Gables property Corp is leasing office buildings with an area of
`49x^2 + 70x+25`

⇒ Area =
`49x^2 + 70x+25`

we can write this as:

Area =
`(7x)^2+2\cdot (7x) \cdot (5) + (5)^2` .....[1]

Use the identity formula:

`(a+b)^2 = a^2+2ab +b^2`

then, by using this formula in [1] we have;

Area =
`(7x+5)^2`

or

Area =
`(7x+5)(7x+5)` square units

Area of building =
`l * w` where l is the length and w is the width respectively;

⇒
`l = w = 7x+5` units

Therefore, the possible length and width of the building is;

l = 7x+5 units

w = 7x+5 units

As we know that the Area of a square is equal to side times side . Since each side of a square is the same, it can simply be the length of one side squared.

Therefore, the possible shape of the building is Square.