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AleksandrR [38]
3 years ago
14

Find the value of the variable if P is between J&K JP=8z-17; PK=5z+37; JK=17z-4

Mathematics
1 answer:
pochemuha3 years ago
5 0
Because P it between J and K it means that JP+PK = JK. That means:
8z-17+5z+37=17z-4
13z+20=17z-4
4z=24
z=6

<span>The value of the variable is 6.</span>
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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.
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Let
x,y, and z the long sides of the triangle 

we know that

x+y+z=170 ft------> equation 1
x/y=25/14----> y=14x/25------> equation 2
y/z=14/12-----> equation 3
x/z=25/12----> z=12x/25------> equation 4

substitute equation 2 and equation 4 in equation 1
x+[14x/25]+[12x/25]=170------> multiply by 25 both sides
25x+14x+12x=4250
51x=4250
x=4250/51
x=250/3
y=14x/25------> y=(250/3)*(14/25)----> y=140/3
z=12y/14-----> (140/3)*12/14----> z=40

Using Heron's formula,
Area of the triangle = √s (s-a) (s-b) (s-c)
where s is the semiperimeter
s=170/2-----> s=85 ft
Area=√85*[85-250/3]*[85-140/3]*[85-40]
Area=9.22*[1.67]*[38.33]*[45]------> Area=26558.21 ft²

the answer is
26558.21 ft²
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