Question

the are of a triangle is jointly related to the height and the base of the triangle. if the base is increased 10% and the height is decreased by 10%. what will be the percentage change of the area.


way to answer

Equation:





Representation:






Solution:






Final answer:

Answer 1

Answer:

0099461659192883838282883

Step-by-step explanation:

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Answer 2

Equation:

Area of triangle: A = 1/2 × (b × h)

Representation:

b = base of the triangle

h = height of the triangle

Solution:

The base is increased 10% and the height is decreased by 10%.

$Final \: area \: A' = \frac{1}{2} \times (b + \frac{b}{10} ) \times (h - \frac{h}{10 } ) \\ = \frac{1}{2} \times \frac{11 \: b}{10} \times \frac{9 \: h}{10} \\ = \frac{99}{100} \times \frac{1}{2} \times b \times h \\ A' = \frac{99}{100} \times A$

$change \: in \: area = |A' - A | = | \frac{99}{100}A - A | = | \frac{ A }{100} | \\ percentage \: of \: change \: in \: area = \frac{ \frac{A}{100} }{A} \times 100 = 1$

Final answer:

The percentage change of the area is 1%.