Question

if the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square. the area of this square will be 40cm^2 greater than the area of the rectangle. Find the area of the rectangle.

Answer 1

steps explanations: x - 4 = y + 5 (sides of a square)

(x - 4)(y + 5) = 40

Which gives;

(y + 5) (y + 5) = 40

y² + 10y + 25 = 40

y² + 10y + 25 - 40 = 0

y² + 10y - 15 = 0

a=1 b=10 and c=-15

Answer 2

Answer: 30 cm^2.

Explanation:

Let the original length of the rectangle be l and its width be w. Then, according to the problem:

(l - 4) = (w + 5) (equation 1)

Also, the area of the square is 40 cm^2 more than the area of the rectangle. Mathematically, we can represent this as:

(l - 4 + 5)^2 = lw + 40

Simplifying the left-hand side and substituting equation 1, we get:

l^2 - 2lw + w^2 = lw + 40

l^2 - 3lw + w^2 - 40 = 0

(l - 8)(l - 5) = 0

Therefore, l = 8 or l = 5. If we substitute l = 8 into equation 1, we get:

w = (l - 4) - 5 = -1

This is not a valid solution since the width cannot be negative. Therefore, the only valid solution is l = 5, which gives:

w = (l - 4) + 5 = 6

So the area of the rectangle is:

A = lw = 5 x 6 = 30 cm^2.