Question

A square has sides of length s. A rectangle is 6 inches shorter and 1 inch longer than the square. Which of the following expressions represents the area of the rectangle? Select all that apply.
S^2

(s+6)(s+1)

(s-6)(s-1)

(s-6)(s+1)

s^2 - 7s + 1

s^2 - 5s - 6

s^2 + 7s + 6

Answer 1

Answer: Area of rectangle can be given by expressions:

$(s-6)(s+1)\text {and }s^2-5s-6$

Step-by-step explanation:

Given : A square has sides of length s.

According to the question,

Dimensions of new rectangles=(s-6)×(s+1)

Thus, Area of rectangle= (s-6)×(s+1)

$=s^2-6s+s-6\\\Rightarrow\ s^2-5s-6$

Thus , area of rectangle can be given by expressions:

$(s-6)(s+1)\text {and }s^2-5s-6$

Answer 2

Answer:

(s-6)(s+1) and s² - 5s - 6

Step-by-step explanation:

Suppose s represents the side length of the square,

∵ Rectangle is 1 inch longer than the square,

⇒ Length = (s+1) inches,

It is 6 inches shorter than square,

⇒ Width = (s-6) inches

∵ Area of a rectangle = Length × width

= (s+1)(s-6)

= s² - 6s + 1s - 6

= s² - 5s - 6

Hence, THIRD and FIFTH options are correct.