Problema Solution
A wire of length 100cm is cut in to two parts and each part is bent to form a square. If the sum of squares is 425cm^ find the lengths of the side of the two squares.
Answer provided by our tutors
Let
x = the length of the side of the first square, x>0
y = the length of the side of the second square, y>0
A wire of length 100cm is cut in to two parts:
4x + 4y = 100 divide both sides by 4
x + y = 100
y = 25 - x
we will assume that the sum of the areas of the two square is 425 cm^2:
x^2 + y^2 = 425
plug y = 25 - x into the last equation:
x^2 + (25 - x)^2 = 425
by solving the above equation we find:
x1 = 20 cm
x2 = 5 cm
click here to see the step by step solution of the quadratic equation:
for x = 20 cm y = 25 - 20 = 5 cm
for x = 5 cm y = 25 - 5 = 20 cm
thus we conclude the lengths of the sides of the two squares are 20 cm and 5 cm.