Question 575465
2. If each side of a square is increased by 2 cm, the total area of both the new square and the original square will be 400 cm2.
Approximate to the nearest tenth of a centimeter the length of each side of the original square.
:
let x = side of the smaller square
then
(x+2) = side of the larger square
:
(x+2)^2 + x^2 = 400
FOIL
x^2 + 4x + 4 + x^2 - 400 = -
Combine like terms
2x^2 + 4x - 396 = 0
Simplify, divide by 2
x^2 + 2x - 198 = 0
Use the quadratic formula to find
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1; b=2; c=-198
{{{x = (-2+- sqrt(2^2-4*1*-198 ))/(2*1) }}}
do the math here, the positive solution:
x = 13.1 cm
:
:
Check this by finding the area of each square
13.1^2 = 171.61
15.1^2 = 228.01
----------------
total A: 399.62 ~ 400