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

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Rasheed
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54 Answers
Let the original base of the triangle be b and the original height be h .
Given that the new base decreases by 20% and the new height increases by 30%, the new base is 0.8b and the new height is 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, we have:
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 or 5+3 = 8 .
Therefore, the sum of the measurements of the base and height is \boxed{8} .

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