Answer: 210 square inches
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Step-by-step explanation:
Check out the attached image. I've added in points A through D. The points A,B,C are the vertices of the largest triangle. Point D is directly below point A, and point D is on segment BC.
To find the area of the largest triangle ABC, we need the base length BC, which is broken up into segments x and y
x = length from C to D
y = length from D to B
Let's find x first
Triangle ADC is a right triangle, so we can use the pythagorean theorem
a^2 + b^2 = c^2
x^2 + 15^2 = 17^2
x^2 + 225 = 289
x^2 = 289 - 225
x^2 = 64
x = sqrt(64)
x = 8
Follow similar steps to find y
a^2 + b^2 = c^2
y^2 + 15^2 = 25^2
y^2 + 225 = 625
y^2 = 625 - 225
y^2 = 400
y = sqrt(400)
y = 20
Therefore
BC = x+y
BC = 8+20
BC = 28
The base of the triangle ABC is BC = 28 units
b = base
b = 28
The height is AD = 15
h = height
h = 15
We can now find the area of triangle ABC
Area = b*h/2
Area = 28*15/2
Area = 420/2
Area = 210
The area of the triangle is 210 square inches