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A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the triangle?
Recognize it as a right triangle (7, 24, 25 is a Pythagorean triple).
A rectangular garden is to be fenced, with the length being 3 times the width. If 64 meters of fencing is available, what is the maximum area of the garden?
A company offers two salary plans: Plan A pays $500 per week plus 5% commission on sales, Plan B pays $300 per week plus 8% commission. For what amount of sales do both plans yield the same total pay?
We seek the smallest three-digit integer satisfying this condition. The smallest three-digit number is 100. We check:
LCM takes the highest power of each prime:
But 24 is the greatest common divisor of all such products (since 24 divides all, and 24 itself achieves it).
Question: In a right triangle, the hypotenuse is $ y $, and the inradius is $ d $. What is the ratio of the area of the incircle
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