4. Find two consecutive positive integers, sum of whose squares is 30).
5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find
the other two sides,
6. A cottage industry produces a certain number of pottery articles in a day. It was observed
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Answer:
Step-by-step explanation:
Let x be the base of the triangle, then the altitude will be (x−7).
By Pythagoras theorem,
x
2
+(x−7)
2
=(13)
2
2x
2
−14x+49−169=0
2x
2
−14x−120=0
x
2
−7x−60=0
−12x+5x−60=0
(x−12)(x+5)=0
x=12,x=−5
Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and the altitude of the triangle will be 12−7=5cm.
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