Question

Calculate the area and perimeter of the shaded region​

Answer 1

Answer:

Explanation:

For a rectangle, area is A = lw and perimeter is P=2l+2w, where l is the length and w is the width.

Let x = length and x-4 = width.

The area equation to solve becomes x(x-4)=96, or x^{2}-4x-96=0.

To factor, find two numbers the sum to -4 and multiply to -96. -12 and 8 will work:

x2 + 8x - 12x - 96 = 0

x(x + 8) - 12(x + 8) = 0

(x - 12)(x + 8) = 0

Set each factor equal to zero and solve:

x=12 or x=-8.

Therefore the length is 12\; cm and the width is 8 \; cm, giving a perimeter of 40\; cm.