In the rectangular coordinate system above the area of PQR is what fraction of the area of LMN
From the attached figure we find the area of PQR and area of LMN
WE know the formula for area of triangle =
* base * height
In the triangle PQR,
Base PR= 4
Height = distance between x- axis and point Q = 4
Area of the triangle PQR =
* 4 * 4 = 8
Similarly we find the area of LMN
In the triangle LMN,
Base LN= 12
Height = distance between x- axis and point M = 12
Area of the triangle LMN =
* 12 * 12 = 72
Hence ,
= 
Area of PQR =
of the area of LMN
Transpose the constant on the left hand side of the equation to the right side. The equation becomes x² = 45 + 4,
x² = 49
x = sqrt(49)
x = 7 and x = -7
Only -7 is on the choices. Thus, the answer is x = -7.
Answer:
The width is 5.25 feets
Step-by-step explanation:
The dimensions of the two rectangular wooden boards that Elenor and Max used to make a set for the school play are shown in the attached photo. The widths of the two boards are equal. The lengths are 6 feets and 51/2 feets
Area of each rectangular length, L × Width, W
Area of the longer rectangular board
= 6x W = 6W feet^2
Area of the shorter rectangular board
= 11/2 x W = 11W/2 feet^2
The area of the set is 60-3/8 square feet. This is equal to 483/8 feet^2.
Therefore,
483/8 = 6W + 11W/2 = 23W/2
8 × 23W = 483 × 2
184W = 966
W = 966/184 = 5.25 feets