Lower and upper bounds?

Question

The base of a triangle is 9 cm correct to the nearest cm. The area of this triangle is 40 cm2 correct to the nearest 5 cm2.
Calculate the upper bound for the perpendicular height of this triangle

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Answer 1 · 2018-05-02T17:43:31

#10cm#

base of triangle,#b#

#b=9cm " nearest cm"#

#:.8.5<=b<9.5#

area #A#

#A=40cm^2 " nearest "5cm^2#

#:.37.5<=A<42.5#

the upper bound for perpendicular height #h#

#A=1/2bh#

#=>h=(2A)/b#

since we require the upper bound we want the biggest possible value for #h#

#h_(upp)=(2xx42.5)/8.5#

#h_(upp)=10cm#