Answer:
A and D
Step-by-step explanation:
<u>A: 12-7=5</u>
B: 13-6=7
C: 11-8=3
<u>D 14-9=5</u>
Have a Fantastic Day! :D
1. 3*3 + 3*8 = 9+24=33
2. 4*4+.5*2*4+5*5= 16+4+25=45
3. 5*10+4*10= 90
4. 24+.5*4*4 = 32
<em><u>The equations used to find the length of leg of triangle are:</u></em>
![0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100](https://tex.z-dn.net/?f=0.5x%28x%2B2%29%20%3D%2024%5C%5C%5C%5Cx%5E2%2B2x-48%3D0%5C%5C%5C%5Cx%5E2%2B%28x%2B2%29%5E2%20%3D%20100)
<em><u>Solution:</u></em>
From given,
Area of right triangle = 24 square feet
Also from given figure in question (attached below )
base = x and height = x + 2
<em><u>The area of triangle is given by formula:</u></em>
![Area = \frac{1}{2} \times base \times height](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20base%20%5Ctimes%20height)
Substituting the values we get,
![24 = \frac{1}{2} \times x \times (x+2)\\\\24 = 0.5x(x + 2)\\\\48 = x(x+2)\\\\x^2 + 2x - 48 = 0\\\\](https://tex.z-dn.net/?f=24%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20x%20%5Ctimes%20%28x%2B2%29%5C%5C%5C%5C24%20%3D%200.5x%28x%20%2B%202%29%5C%5C%5C%5C48%20%3D%20x%28x%2B2%29%5C%5C%5C%5Cx%5E2%20%2B%202x%20-%2048%20%3D%200%5C%5C%5C%5C)
<em><u>Also, the above equation can be written as,</u></em>
![x^2 + (x+2)^2 =100](https://tex.z-dn.net/?f=x%5E2%20%2B%20%28x%2B2%29%5E2%20%3D100)
<em><u>Thus the equations used to find the length of leg of triangle are:</u></em>
![0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100](https://tex.z-dn.net/?f=0.5x%28x%2B2%29%20%3D%2024%5C%5C%5C%5Cx%5E2%2B2x-48%3D0%5C%5C%5C%5Cx%5E2%2B%28x%2B2%29%5E2%20%3D%20100)