Answer: 129 Feet
Step-by-step explanation:
You can make an equation where Height=h, and Base=b. So going backwards with the first question, the base will equal 4 times the height: b=4h, and 11 less. b=4h-11. The the other equation will be just that the base plus the height is 49. b+h=49. Then you put that into y=mx+b form. The first equation already is, and the second equation would be b=49-h. So, since the equations equal the same things, you throw away the b. Then you make a new equation by having 4h-11 equal 49-h. Since this is true seeing as they are the same triangle. Then you just use propreties of equality for the equation. You end up with 5h=60. The. You divide 60 by 5 to make 5h just equal h. So you get h=6. Then, like the qeuation said, the base (unknown) plus the height (6) is 49. So to get from 6 to 49, the answer is 43. The formula for that area of a triangle is (base x height) /2 = area. So 43 times 6 is 258. Then divided by 2 is 129. So the area of the triangle is 129.
The area of the triangle is 222 square feet.
The formula for calculating the area of the triangle is expressed as:
A = 0.5bh
The base of a triangle is eleven feet less than four times its height,
b = 4h - 11
Also, if the sum of the lengths of the base and height of the triangle is 49 is expressed as:
b + h = 49
4h-11+h = 49
5h = 49 + 11
5h = 60
h = 12
Since 4h = b + 11
4(12) = b + 11
b = 48 - 11
b = 37
A = 0.5(12)(37)
A = 222ft^2
Hence the area of the triangle is 222 square feet.
Learn more on area of triangle here: https://brainly.com/question/17335144
