The sum of the base and the height of a triangle is 30 cm. find the dimensions for which the area is a maximum. the triangle with the maximum area has a height of and a base of

If the sum of the base and the height are 30, then b+h=30 or h=b-30.

Remember that the area of any triangle is A=½bh.

If you substitute in b-30 for h, then you create a function for the area in terms of the base.

A = ½b(30-b)=15b-½b2

The maximum area would be at the vertex of the parabola that would result from the function.  We can graph to find the max, but there is a simple formula for the x-coordinate of the vertex: -b/2a where b=the linear coefficient and a=the quadratic coefficient.

-15/2(-½)=15  meaning that a base of 15cm would provide the maximum area.  The corresponding height would be 30-15 or 15cm as well.

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d is the answer

step-by-step explanation:

answer

a) the midrange of the data set shown is 85.5

step by step explanation

let's find the midrange.

the midrange is nothing but add the greatest value and the least value, then divide it by 2.

here the greatest value = 99

the least value = 72

midrange = (99 + 72)/2

= 171/2

midrange = 85.5

you.