two squares have sides p cm and (p+5) cms. the sum of theirs squares is 625 sq.cm. the sides of the squares are
Let's call the side length of the first square as "p" cm. According to the problem, the side length of the second square is (p+5) cm.
The sum of their squares is 625 sq. cm. This means we can set up the equation:
p^2 + (p+5)^2 = 625
Expanding the equation:
p^2 + p^2 + 10p + 25 = 625
Combining like terms:
2p^2 + 10p + 25 = 625
Subtracting 625 from both sides:
2p^2 + 10p - 600 = 0
Divide the entire equation by 2 to simplify:
p^2 + 5p - 300 = 0
Now, we need to solve this quadratic equation. We can either factorize it or use the quadratic formula:
Factoring:
(p - 15)(p + 20) = 0
Therefore, p = 15 or p = -20.
But the side length of the square cannot be negative, so we discard p = -20.
Hence, the side length of the square is p = 15 cm.
The side length of the second square is (p+5) cm, so (15+5) cm = 20 cm.
Therefore, the sides of the squares are 15 cm and 20 cm.
To find the sides of the squares, we can set up an equation based on the given information.
Let's consider the first square with side p cm. Its area is p^2 square cm.
The second square has side (p+5) cm. Its area is (p+5)^2 square cm.
According to the information given, the sum of their areas is 625 sq.cm. Therefore, the equation is:
p^2 + (p+5)^2 = 625
To solve this equation, we need to expand the expression (p+5)^2 and simplify:
p^2 + p^2 + 10p + 25 = 625
Combining like terms, we get:
2p^2 + 10p + 25 = 625
Now, we can bring all terms to one side to form a quadratic equation:
2p^2 + 10p + 25 - 625 = 0
Simplifying further:
2p^2 + 10p - 600 = 0
Let's divide every term by 2 to simplify the equation:
p^2 + 5p - 300 = 0
Now, we can apply the quadratic formula to find the values of p:
p = (-b ± √(b^2 - 4ac))/2a
For our equation, a = 1, b = 5, and c = -300. Plugging these values into the quadratic formula:
p = (-5 ± √(5^2 - 4 * 1 * -300)) / 2 * 1
Simplifying further:
p = (-5 ± √(25 + 1200)) / 2
p = (-5 ± √(1225)) / 2
p = (-5 ± 35) / 2
This gives us two possible values for p. By substituting them back into the original equation and solving, we can find the sides of the squares.
p^2 + p^2 + 10 p + 25 = 625
2 p^2 + 10 p - 600 = 0
p^2 + 5 p - 300 = 0
(p+20)(p-15)= 0