Question

There are 2 Rectangles, a red one and a blue one.The Blue rectangle has the perimeter of 250 km. If the area of the red rectangle is 2,500 square kilometers, what are its dimensions?

(Both of the rectangles have the same perimeter)

Answer 1

length = 100

width = 25

Explanation:

Let L = length of red rectangle

Let H = height of red rectangle

Equation1: L+H=125 : we know the perimeter is 250 so L+H is 125

Equation2: L*H=2,500 : we know the area is 2,500

Equation3: L=125-H : subtracted H from both sides of Equation1

Equation4: (125-H)*H=2,500 : substituted "125-H" for L into Equation2

Solve equation4:

(125-H)*H=2,500 multiple terms on left side of equation

125H - H^2 = 2,500 rearrange into standard form

H^2 - 125H + 2,500 = 0

At this point you can "brute force" the answer with the quadratic formula:

H = (125 ± SQRT(125^2 - 4*1*2500) ) / 2

H = 100 or H = 25 : actually these are L and H

You could also factor the equation:

(H - 100) * (H - 25) = 0 : gives same answe

Answer 2

Answer:a

Explanation: