Mrs. Jones is building a deck behind her house. Top 28 ft; Right 25 ft; Bottom 4 ft. What is the length of the unlabeled Left side of this deck?
Ans. 7 ft.
Book's explanation: 〖25〗^2-〖24〗^2=625-576=49=7
Where did they get 24 from? Thank you for your help!
I can't picture the deck. Top? Bottom?
All I can say is that 24 = 28-4, the difference between top and bottom.
But the 7^2+24^2=25^2 seems to be for the legs and diagonal of a triangle. Oh, well, maybe you have a diagram in front of you.
New tile is being laid on a floor that is 12 ft. long and 9 ft. wide. Each square tile measures 9 inches on each side. How many tiles will be needed?
Ans. 192
Please tell me how they got 192
Thank you.
PS digressing
how do I sent you diagrams, i.g., triangle diagram of a deck?
To find the length of the unlabeled side of the deck, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs (the shorter sides) is equal to the square of the hypotenuse (the longest side). In this case, the hypotenuse is the side labeled "Top" and the legs are the side labeled "Right" and the unlabeled side.
The Pythagorean theorem formula is given by: c^2 = a^2 + b^2, where c is the hypotenuse and a and b are the legs.
In this problem, the Top side is given as 28 ft, the Right side is given as 25 ft, and we need to find the length of the Left side.
Let's call the length of the Left side "x". Using the Pythagorean theorem formula, we can write the equation:
x^2 = 28^2 - 25^2
Now, let's solve for x:
x^2 = 784 - 625
x^2 = 159
x ≈ √159
x ≈ 12.61 ft
However, according to the book's explanation, they calculated the length as 7 ft. It seems they mistakenly used 24 instead of 25 for the Right side.
If we use the correct value of 25 for the Right side, the equation becomes:
x^2 = 28^2 - 25^2
x^2 = 784 - 625
x^2 = 159
x ≈ √159
x ≈ 12.61 ft
Therefore, the correct length of the unlabeled Left side of the deck should be approximately 12.61 ft, not 7 ft as mentioned in the book's explanation.