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rubincain203
23.07.2019 •
Mathematics
In δpqr, pq = 17 in, pr = 10 in, qr = 21 in. find the altitude from p to the side qr
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Ответ:
Half perimeter of the triangle is:
s=(17+10+21)/2
s=24
Area of the triangle will be:
A=√s(s-PR)(s-PQ)(s-QR)
A=√(24×7×3×14)
A=84
But:
A=1/2*base*height
hence:
84=1/2×21×h
⇒h=(2×84)/21=8
Ответ:
PS = Sqrt {(PQ)^2-(QS)^2} = Sqrt {(PR)^2-(RS)^2}
Therefore,
Sqrt {(PQ)^2-(QS)^2} = Sqrt {(PR)^2-(RS)^2) => (PQ)^2-(QS)^2 = (PR)^2-(RS)^2
But, PQ= 17 in, QS+RS = QR = 21 in => QS = 21-RS, PR = 10 in
Substituting,
17^2 - (21-RS)^2 = 10^2-(RS)^2 => 289-(21-RS)(21-RS) = 100 -(RS)^2
289-(441-42RS +(RS)^2) = 100- (RS)^2 => 289-441+42RS-(RS)^2 = 100 -(RS)^2 => -152+42RS = 100 => 42RS = 252 => RS = 6 in
Then, QS = 21-6 = 15 in
Finally,
PS (altitude) = Sqrt {17^2-15^2} = 8 in
Ответ:
Table max area = 46 7/8 ft
Table length= 7 1/2 ft
Using area formula, the calculation for maximal width would be:
length * max width = max area
7 1/2 ft * max width = 46 7/8 ft
max width = 46.875/ 7.5 = 6.25ft
The answer to this question would be yes, she can buy a table with more than 6 ft width. But it should not more than 6.25ft width