Question 1146985
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Since the area is a whole number and the hypotenuse is 1 foot longer than one of the sides, the side lengths are almost certainly a Pythagorean triple.<br>
One of the smallest Pythagorean triples satisfies all the conditions of the problem; 7-24-25.<br>
The area is (1/2)(7)(24) = 84
The hypotenuse is 1 foot longer than one of the sides.<br>
Brute force calculations or a calculator show that x=24 is a root of the equation shown in (a).<br>
ANSWERS:
(a) yes; 24 is a root of that equation
(b) yes; 24 is less than 28
(c) 7, 24, and 25<br>