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It has been discovered that a certain cornfield created in the​ 18th-century was a right triangle. One leg of the triangle was formed by a 210 ft long walking trail. The hypotenuse of the triangle was 90 ft longer than the other leg. What were the dimensions of the​ cornfield?

Respuesta :

Explanation:

Given that,

Let ABC is a triangle such that AB is perpendicular distance, BC is base and AC is the hypotenuse of triangle.

Let AB = 210 ft

AC = 90 + x

BC = x

To find :

The dimensions of the​ cornfield.

Solution :

Pythagoras theorem is used to find the value of x. It is given by :

[tex]AB^2+BC^2=AC^2[/tex]

[tex](210)^2+x^2=(90+x)^2[/tex]

On solving the above equation we find the value of x, x = 200 ft

So, BC = 200 ft

AC = 90 + 200 = 290 ft

So, the length, base and the hypotenuse of the triangle is 210 ft, 200 ft and 290 ft respectively.

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