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carlosego genius 11.6k answer 175.7m people helped the perimeter is the sum of the sides: P=(x-7) +(x+1)+(x) rewriting: P=3x-6 the area is giving by:A=(1/2)*(x-7)*(x) the area and the perimeter are the same: (1/2)*(x-7)*(x)=3x-6 rewriting: (x-7)*(x)=6x-12 x^2-7x-6x+12=0 x^2-13x+12=0 polynomial of degree 2, therefore there are 2 possible solutions. Viable solution. Viable solution: x=12 sides of triangle: 5 12 13
The factors of seven are 1 and 7
Answer:
The area of the rectangle is 42 units^2
Step-by-step explanation:
we know that
The area of rectangle is equal to
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
In this problem
AB=DC
BC=AD
see the attached figure with letters to better understand the problem
we have that
![L=BC\\W=AB](https://tex.z-dn.net/?f=L%3DBC%5C%5CW%3DAB)
the formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
we have the points
![A(2,-1),B(5,2),C(12,-5),D(9,-8)](https://tex.z-dn.net/?f=A%282%2C-1%29%2CB%285%2C2%29%2CC%2812%2C-5%29%2CD%289%2C-8%29)
<em>Find out the distance BC</em>
we have
![B(5,2),C(12,-5)](https://tex.z-dn.net/?f=B%285%2C2%29%2CC%2812%2C-5%29)
substitute in the formula
![d=\sqrt{(-5-2)^{2}+(12-5)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-5-2%29%5E%7B2%7D%2B%2812-5%29%5E%7B2%7D%7D)
![d=\sqrt{(-7)^{2}+(7)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-7%29%5E%7B2%7D%2B%287%29%5E%7B2%7D%7D)
![d_B_C=\sqrt{98}\ units](https://tex.z-dn.net/?f=d_B_C%3D%5Csqrt%7B98%7D%5C%20units)
<em>Find out the distance AB</em>
we have
![A(2,-1),B(5,2)](https://tex.z-dn.net/?f=A%282%2C-1%29%2CB%285%2C2%29)
substitute in the formula
![d=\sqrt{(2+1)^{2}+(5-2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%282%2B1%29%5E%7B2%7D%2B%285-2%29%5E%7B2%7D%7D)
![d=\sqrt{(3)^{2}+(3)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%283%29%5E%7B2%7D%2B%283%29%5E%7B2%7D%7D)
![d_A_B=\sqrt{18}\ units](https://tex.z-dn.net/?f=d_A_B%3D%5Csqrt%7B18%7D%5C%20units)
<em>Find out the area</em>
![A=(L)(W)](https://tex.z-dn.net/?f=A%3D%28L%29%28W%29)
we have
![L=d_B_C=\sqrt{98}\ units](https://tex.z-dn.net/?f=L%3Dd_B_C%3D%5Csqrt%7B98%7D%5C%20units)
![W=d_A_B=\sqrt{18}\ units](https://tex.z-dn.net/?f=W%3Dd_A_B%3D%5Csqrt%7B18%7D%5C%20units)
substitute
![A=(\sqrt{98})(\sqrt{18})=42.0\ units^2](https://tex.z-dn.net/?f=A%3D%28%5Csqrt%7B98%7D%29%28%5Csqrt%7B18%7D%29%3D42.0%5C%20units%5E2)