Question
If the base of a triangle decreases by 20% and the height relative to said base increases by 30%, then its area changes by 0.3 cm2 . Calculate the sum of the measurements of the base and height mentioned, if it is known that they are integers and different from the unit
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Answer to a math question If the base of a triangle decreases by 20% and the height relative to said base increases by 30%, then its area changes by 0.3 cm2 . Calculate the sum of the measurements of the base and height mentioned, if it is known that they are integers and different from the unit
Rasheed
4.7110 Answers
Let the original base of the triangle be b h
Given that the new base decreases by 20% and the new height increases by 30%, the new base is 0.8b 1.3h
The original area of the triangle is \frac{1}{2}bh
The new area of the triangle is \frac{1}{2}(0.8b)(1.3h) = 0.52bh
Given that the area changes by 0.3 cm^2
0.52bh - \frac{1}{2}bh = 0.3
0.02bh = 0.3
bh = 15
Since the base and height are integers and different from one another, possible combinations are:
b = 3, h=5 \text{ or } b=5, h=3
Sum of the measurements of the base and height is 3+5 = 8 5+3 = 8
Therefore, the sum of the measurements of the base and height is \boxed{8}
Given that the new base decreases by 20% and the new height increases by 30%, the new base is
The original area of the triangle is
The new area of the triangle is
Given that the area changes by 0.3 cm
Since the base and height are integers and different from one another, possible combinations are:
Sum of the measurements of the base and height is
Therefore, the sum of the measurements of the base and height is
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