Question

Sum of the areas of two squares to 60 metre square if the difference of their perimeter is 24 metre then find the side of the square

Answer 1

Answer:

Let x be side (in meters) of Square 1.

Let y be side (in meters) of Square 2.

x²+y²=60 -------------------1

4x + 4y = 24 --------------2

From equation 2,

4(x+y)=24

x+y = 24/4

x+y = 6 -------------3

From equation 3,

y = 6-x ---------------4

Substitute equation 4 in equation 1

x² + (6-x)² = 60

x²+ 6²+x²- 2*6*x = 60

2x²-12x+36=60

2x²-12x = 60-36

2x²-12x = 24 ------------------5

Divide equation 5 by 2,

x² - 6x = 12

x²-6x-12=0

a=1

b=-6

c=-12

Quadratic formula, -b ± √b²-4ac /2a

-(-6)±√36+48 /2

6±√84 /2

6+√84 /2  = 3+√21

6-√84 /2  = 3-√21

Side can't be negative.

∴x= 3+√21

From equation 4,

y=6-x

y=6-3√21

y=3(2-√21)

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