Question

4. Consider the right triangle below.

Answer 1

Answers:

• x = 1031/55 = 18.74545 approximately
• area = 35,542.92 square units approximately

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Explanation:

The perimeter is the sum of the exterior sides. We'll add up these three sides

• 16x+27
• 14x-45
• 25x

and set the sum equal to the perimeter 1013

The equation we need to solve is

(16x+27)+(14x-45)+(25x) = 1013

Solving for x leads to...

(16x+27)+(14x-45)+(25x) = 1013

16x+27+14x-45+25x = 1013

(16x+14x+25x)+(27-45) = 1013

55x-18 = 1013

55x = 1013+18

55x = 1031

x = 1031/55

x = 18.74545 approximately

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Use this x value to find the length of each side. I'll use the decimal form of x. We get the following side lengths:

• 16x+27 = 16*(18.74545) + 27 = 326.9272
• 14x - 45 = 14*(18.74545) - 45 = 217.4363
• 25x = 25*(18.74545) = 468.63625

Those values are approximate.

We can then find the area of the triangle

area = (1/2)*base*height

area = (1/2)*(326.9272)*(217.4363)

area = 35,542.92036868

area = 35,542.92

The area is approximate as well.

Answer 2

Answer:

16x+27+14x-45+25x=1013 units

X= 18.75

Area= b × h × (1/2)

A= 1/2 × 327 × 217.5 = 35561.25 units^2