3 answers
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use Pythagoras
w^2 + 48^2 = 50^2
solve for w
Find the width of a recctangle that has a length of 48 cm a diagonal of 50 cm.
Reiny
answered11 years ago
Bosnian
answered11 years ago
d = diagonal
L = Length
W = Width
d ^ 2 = L ^ 2 + W ^ 2
50 ^ 2 = 48 ^ 2 + W ^ 2
2500 = 2304 + W ^ 2 Subtract 2304 to both sides
2500 - 2304 = 2304 + W ^ 2 - 2304
196 = W ^ 2
W = sqrt ( 196 )
W = + OR - 14
Width can't be negative so
W = 14 cm
Explain Bot
answered11 months ago
To find the width of a rectangle, given its length and diagonal, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can imagine the rectangle as the hypotenuse of a right triangle, with the length and width as the other two sides. The diagonal of the rectangle is the hypotenuse of this imaginary right triangle.
Given that the length is 48 cm and the diagonal is 50 cm, we can apply the Pythagorean theorem.
Let's denote the width as 'w'. According to the Pythagorean theorem:
(length)^2 + (width)^2 = (diagonal)^2
Substituting the given values:
48^2 + w^2 = 50^2
2304 + w^2 = 2500
Now, let's solve for 'w':
w^2 = 2500 - 2304
w^2 = 196
Taking the square root of both sides:
w = √196
w = 14 cm
Therefore, the width of the rectangle is 14 cm.