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kkurt [141]
3 years ago
5

Triangle QRS, with vertices Q(6, -2), R(4, -7), S(2, -5), is drawn inside a rectangle, . What is the area, in square units, of t

riangle QRS?
HELP!
Mathematics
1 answer:
CaHeK987 [17]3 years ago
3 0
We look for the distance between each one of the vertices applying the following formula:
 d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
 For QR:
 
QR = root ((4-6) ^ 2 + (-7 + 2) ^ 2)
 QR = 5.385164807
 For QS:
 
QS = root ((2-6) ^ 2 + (-5 + 2) ^ 2)
 QS = 5
 For RS:
 
RS = root ((2-4) ^ 2 + (-5 + 7) ^ 2)
 RS = 2.828427125
 Now we apply the heron formula:
 A = root (s * (s-a) * (s-b) * (s-c))
 Where,
 s = (a + b + c) / 2
 s = (5.385164807 + 5 + 2.828427125) / 2
 s = 6.606795966
 Substituting:
 A = root (6.606795966 * (6.606795966-5.385164807) * (6.606795966-5) * (6.606795966-2.828427125))
 A = 7.00000000
 A = 7 units ^ 2
 Answer:
 
The area, in square units, of triangle QRS is:
 
A = 7 units ^ 2
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Angelo is making a rectangular floor for a clubhouse with an area of 84 square feet. The length if each side of the floor is a w
Alexxandr [17]

Answer:

L=1 ft and B=84 ft

L=2 ft and B=42 ft

L=4ft and B=21ft

L=6ft and B=14 ft

L=7ft and B=12ft

L=12 ft and B=7ft

L=14ft and B=6 ft

L=21 ft and B=4 ft

L=42 ft and B=2 ft

L=84 ft and B=1 ft

Step-by-step explanation:

We are given that

Area of rectangular floor=84 square feet

We have to find the possible length and width of for Angelo's clubhouse.

Area of rectangle=length\times breadth

Using the formula

Area of rectangular floor for clubhouse=84 square feet

Length(L)\times breadth(B)=84

Factor of 84 are

1,2,4,6,7,12,14,21,42,84

Therefore,  possible dimension of rectangular floor

1ft\times 84ft,2ft\times 42ft,4ft\times 21ft,6ft\times 14ft,7ft\times 12ft,12ft\times 7ft,14ft\times 6ft,21ft\times 4ft,42ft\times 2ft,84ft\times 1ft

L=1 ft and B=84 ft

L=2 ft and B=42 ft

L=4ft and B=21ft

L=6ft and B=14 ft

L=7ft and B=12ft

L=12 ft and B=7ft

L=14ft and B=6 ft

L=21 ft and B=4 ft

L=42 ft and B=2 ft

L=84 ft and B=1 ft

5 0
3 years ago
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