The perimeter of a triangle is 170 feet and the sides are in the ratio of 25: 14: 12. find the area of the triangle.

  494.34 ft^2

Step-by-step explanation:

If we assume the given ratio units are actual side lengths, then we can compute the area using Heron's formula:

  A = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are side lengths, and s=(a+b+c)/2

For this triangle, that area is ...

  s = (25 +14 +12)/2 = 51/2 = 25.5

  A = √(25.5(25.5 -25)(25.5 -14)(25.5 -12)) = √(25.5·0.5·11.5·13.5) = √1979.4375

  A ≈ 44.4909 . . . . square ratio units

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The perimeter in ratio units is 2s = 51. The actual perimeter is 170 feet, so the scale factor between ratio units and feet is ...

  (170 ft)/(51 ratio units) = (10/3) ft/ratio unit

The area scale factor is the square of this, so the area in square feet is ...

  (44.4909 units^2)(10/3 ft/unit)^2 = 494.34 ft^2

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

24

step-by-step explanation:

if it takes 8 pounds to make 12 divide 12 by 8 and you get 1.5, 1.5 x 16 = 24