A builder is building a rectangular deck with dimensions of 16 ft by 30 ft. To ensure that the sides form 90 degree angles, what shouls each diagonal measure?
I'm confused on how to answer this.
Use the right angle relatonship>
Diagonal^2=16^2+30^2
diagonal= sqrt ( above)
To find the lengths of the diagonals of a rectangular deck, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right triangle are the length (30 ft) and the width (16 ft) of the deck. Let's call the diagonal d. We can set up the equation as follows:
d^2 = 30^2 + 16^2
To find the value of d, we need to calculate the squares of 30 and 16 first:
30^2 = 900
16^2 = 256
Now, we can substitute these values back into the equation:
d^2 = 900 + 256
d^2 = 1156
To solve for d, we take the square root of both sides:
d = sqrt(1156)
d ≈ 34.02 ft
So, each diagonal of the rectangular deck should measure approximately 34.02 feet.