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Llana [10]
3 years ago
8

An artist is deciding between two different triangular shapes to use for a sculpture. The first triangle has a base of 20 feet a

nd a height of 5 feet. The second triangle has a base of 25 feet. If the two triangles have the same area, what is the height of the second triangle.
Mathematics
2 answers:
sdas [7]3 years ago
6 0
The correct answer is c) 4ft
Katyanochek1 [597]3 years ago
5 0
<span>The first triangle has a base of 20 feet and a height of 5 feet.
</span>A = 1/2bh
A = 1/2(20)(5) 
A = 50

The second triangle has a base of 25 feet, <span>two triangles have the same area

A = 1/2bh
50 =1/2(25) h
50 = 12.5 h
h = 50 / 12.5
h = 4

answer: </span><span>C) 4 ft </span><span>

</span>
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\bf \begin{array}{cccllll} \stackrel{\textit{point (0,-7)}}{-7=a(0)^2+b(0)+c}& \stackrel{point (7,-14)}{-14=a(7)^2+b(7)+c}& \stackrel{point (-3,-19)}{-19=a(-3)^2+b(-3)+c}\\\\ -7=c&-14=49a+7b+c&-19=9a-3b+c \end{array}

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\bf -14=49a+7b-7\implies -7=49a+7b\implies -7-49a=7b \\\\\\ \cfrac{-7-49a}{7}=b\implies \cfrac{-7}{7}-\cfrac{49a}{7}=b\implies -1-7a=b

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\bf -19=9a-3b-7\implies -12=9a-3b\implies -12=9a-3(-1-7a) \\\\\\ -12=9a+3+21a\implies -15=9a+21a\implies -15=30a \\\\\\ -\cfrac{15}{30}=a\implies \blacktriangleright -\cfrac{1}{2}=a \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{and since we know that}}{-1-7a=b}\implies -1-7\left( -\cfrac{1}{2} \right)=b\implies -1+\cfrac{7}{2}=b\implies \blacktriangleright \cfrac{5}{2}=b \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{2}x^2+\cfrac{5}{2}x-7~\hfill

3 0
3 years ago
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