(please give brief explanation to this sentence > two squares have sides p cm and (p+5) cms)
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
what's to explain? Write the facts in symbols:
p^2 + (p+5)^2 = 625
Now just solve for p and find p+5
Sum of squares
= p²+(p+5)²
=625
Expand
p²+p²+10p+25=625
2p²+10p=600
p²+5p-300=0
(p-15)(p+20)=0
p=15 or p=-20, reject negative root
The sides of the squares are therefore:
p=15
p+5=15+5=20
In this sentence, we are given information about two squares. The first square has a side length of "p" centimeters, and the second square has a side length of "(p+5)" centimeters. We need to find the values of "p" and "(p+5)".
To solve this, we can set up an equation based on the given information. We know that the sum of the squares of these two squares is 625 square centimeters.
The area of the first square with side length "p" is given by p^2 (p squared).
The area of the second square with side length "(p+5)" is given by (p+5)^2 ((p+5) squared).
According to the given information, the sum of these two areas is 625 square centimeters. So, we can write the equation as:
p^2 + (p+5)^2 = 625
To solve this quadratic equation, we can expand the expression (p+5)^2 and simplify the equation:
p^2 + p^2 + 10p + 25 = 625
2p^2 + 10p - 600 = 0
Now, we can solve this quadratic equation either by factoring, completing the square, or by using the quadratic formula. Once we find the values of "p", we can substitute it into the expression "(p+5)" to find the sides of the squares.