Question

The perimeter of the rectangle is 80 cm. the area of the rectangle is a cm?.

show that x² - 40х a = 0.

Answer 1

To find the area of a rectangle, substitute the sum of length and width into the area formula. The equation matches x^2 - 40x + a = 0.

Step-by-step explanation:

A rectangle's perimeter can be found by adding up all four sides of the rectangle. If the perimeter of a rectangle is 80 cm, then the sum of all four sides is 80 cm. Let's assume the length of the rectangle is l cm and the width is w cm. The perimeter formula can be written as:

2(l + w) = 80

Dividing both sides by 2, we get:

l + w = 40

The area of a rectangle can be found by multiplying its length and width. Let's substitute l + w with 40 in the area formula:

Area = l * w = lw

Area = (40 - w) * w = 40w - w^2

This equation can be rearranged to match the given equation:

x^2 - 40x + a = 0

So, we can conclude that a = 40w - w^2.