Question

The perimeter of a square s1 is 12m more than the perimeter of the square s2. If the area of s1 equals three times the area of s2 minus 11, what is the perimeter of s1?

Answer 1

Answer:

Perimeter of square s1 = 32 meters

Explanation:

Let the side of the square s1 be x and the side of square s2 be y

We are given that the perimeter of s1 is 12 meters more than the perimeter of s2

This means that:

4x = 4y + 12 ..................> equation I

We can rewrite this equation as:

x = y + 3

y = x - 3 .....................> equation II

We are also given that the area of s1 is 3 times the area of s2 minus 11.

This means that:

x² = 3y² - 11 ..................> equation III

Substitute with equation II in equation III and solve for x as follows:

x² = 3y² - 11

x² = 3(x-3)² - 11

x² = 3(x²-6x+9) - 11

x² = 3x² - 18x + 27 - 11

x² = 3x² - 18x + 16

2x² - 18x + 16 = 0

either x = 8

or x = 1

For x = 8 .................> y = x - 3 = 8 - 3 = 5 ..............> both are accepted

For x = 1 ...........> y = x - 3 = 1 - 3 = -2 ..............> rejected as side cannot be negative

Therefore:

the side of square s1 = 8 m

Perimeter of s1 = 4*8 = 32 meters

Hope this helps :)