what is the length of a diagonal of a rectangular picture whose sides are 3 inches by 4 inches
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
5 = c
3 4 5 right triangle
3^2 + 4^2 = 25 = 5^2
To find the length of the diagonal of a rectangular picture, such as the one described with sides measuring 3 inches by 4 inches, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides.
In this case, the diagonal of the rectangle acts as the hypotenuse of a right-angled triangle, and the two sides of the rectangle form the other two sides.
Let's call the length of the diagonal "d", and the sides of the rectangle "a" and "b".
We have:
a = 3 inches
b = 4 inches
Using the Pythagorean theorem, we can write the relationship as follows:
d^2 = a^2 + b^2
Substituting the values of a and b:
d^2 = 3^2 + 4^2
Simplifying further:
d^2 = 9 + 16
d^2 = 25
To find the length of the diagonal "d", we need to take the square root of both sides of the equation:
d = √25
d = 5 inches
Therefore, the length of the diagonal of the rectangular picture is 5 inches.