Formulate and solve problems involving quadratic equations

Question

Two squares have a combined area of 41m^2. The sum of their perimeter is 36m.

Determine the length of the side of each square.

 

Can you show me the working please?

Answer 1

Hi Jade,

         If you convert the information given into equations we have

S₁= Length of the side of square one S₂ same for square two, then S₁² +S₂²=41 (combined area is 41m²)

and  4S1+4S₂=36 (the sum of the perimeters is 36m)

 

This gives two equations with two unknowns. If you solve the linear equation for S₁=9-S₂ then substitute this in the other equation gives (9-S₂)² + S₂² - 41=0 which is a quadratic equation .  Can you take it from here ?

 

I got S₁=4 or 5 and S₂=5 or 4.

Regards

Jim

 

Answer 2

x = side of one

y = side of other

 

4x + 4y = 36

x + y = 9

y = 9 - x

 

x² + y² = 41    Substitute the "y" from above.

x² + (9 - x)²  = 41

x² + 81 - 18x + x² = 41

2x² - 18x + 81 = 41

2x² - 18x + 40 = 0

x² - 9x + 20 = 0

(x - 4)(x - 5) = 0

x ∈ {4, 5}

 

The side of one is 4 and the side of the other is 5.