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This question boils down to this:
"What is the diagonal of a square with a side length of 90 ft?"
The key to this question is the properties of squares.
All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles.
Now we have two triangles, each with angle measures of 45°, 45°. and 90°.
(an isoceles right triangle)
This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!
In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.
What is the time it takes Sanjay to complete the puzzle? 6 hours
What is the time it takes Felipe to complete the puzzle? 8 hours
We can use the general formula of rate and time to solve this problem. Generally we have,
<em><u>Rate * Time = Work/Job</u></em>
<em>** where Work/Job for this problem is 1 since they are doing 1 work, which is solving a puzzle</em>
- <u>Finding rate of Sanjay:</u>

- <u>Finding rate of Felipe:</u>

Working together, their rate is the sum,
Total Rate =
.
Using the general formula again, we can find the time it will take to solve the puzzle when both works together.
hours
Rounding the answer, we have 3.4 hours.
ANSWER: 3.4 hours