Question

Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.

Answer 1

The correct answer is  8.5 in.

What is Heron's formula in math?

• Heron's formula, formula credited to Heron of Alexandria for finding the area of a triangle in terms of the lengths of its sides.
• In symbols, if a, b, and c are the lengths of the sides: Area = Square root of√s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.

we know that

The formula of area of triangle is equal to

             $A = \frac{1}{2} (b) (h)$

We have

b = BC = 6 in

h = AD = x in

substitute

$A = \frac{1}{2} (6) (x)$

$A = 3x^{2} in^{2} ..................(1)$

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  a,b,c be the lengths of the sides of a triangle.  

The area is given by:-

$A = \sqrt{p(p-a) (p-b) (p-c)}$                     where p is half the perimeter

$p = \frac{a +b+ c}{2}$

a = 9 in , b= 9 in, c = 6 in

$p = \frac{9 + 9 + 6}{2} = 12 in$

Find the area

$A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}$

$A = \sqrt{12 (3)(3)(6)}$

$A = \sqrt{648}$

$A = 25.46 in^{2}$

Substitute the value of the area in the equation 1 and solve for x

$A = 3x in^{2}$

25.46 = 3x

x = 25.46/3

x = 8.5 in

Learn more about Heron's Formula

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