A playground is shaped like a rectangle with a width 5 times it's length (t). What is the simplified expression for the distance between opposite corners of the playground?
a- tsq root 26
b- 5t
c- 26t squared
d- 6t
my answer is d 5t
5t+t =x
x=6t
I went back and checked my figures and I think it should be a t sq root 26
d^2 = t^2 + (5t)^2
= 26t^2
d = t√26 is correct
Let t = length
Let 5t = width
The line that connects the opposite corners of rectangle is the diagonal, and its length can be defined as
d = sqrt(l^2 + w^2)
Thus,
d = sqrt(t^2 + 25t^2)
d = sqrt(26t^2)
d = t * sqrt(26)
Actually you can also use pythagorean theorem to find d, and you should get the same answer.
hope this helps~ `u`
To find the distance between opposite corners of the rectangular playground, we can use the Pythagorean theorem. According to the problem, the width of the rectangle is 5 times its length (t).
Let's assume the length of the rectangle is t.
Then, the width of the rectangle would be 5t.
According to the Pythagorean theorem, the square of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the two sides.
In this case, the two sides are the length (t) and the width (5t), so the distance between opposite corners can be represented by the equation:
Diagonal^2 = length^2 + width^2
Plugging in the values, we get:
Diagonal^2 = t^2 + (5t)^2
Diagonal^2 = t^2 + 25t^2
Diagonal^2 = 26t^2
To simplify this expression, we take the square root of both sides:
Diagonal = √(26t^2)
Now, we can simplify the expression further:
Diagonal = t√26
Therefore, the simplified expression for the distance between opposite corners of the playground is option A: tsq root 26.