The answer is 16.3 cm
Take a look at the image.
The area of the triangle (A) is:
A = b * hb / 2
A = a * ha / 2
So:
b * hb / 2 = a * ha / 2
b * hb = a * ha
We have:
b = 18 cm
ha = 15 cm
a = ?
hb = ?
1. Find hb.
According to the image, a is hypotenuse of the right triangle with sides hb and b/2. Use the Pythagorean theorem:
a² = (b/2)² + hb²
b = 18
a² = (18/2)² + hb²
a² = (9)² + hb²
a² = 81 + hb²
hb² = a² - 81
2. Find a.
b * hb = a * ha
Square both sides
b² * hb² = a² * ha²
b = 18 cm
ha = 15 cm
hb² = a² - 81
(18)² * (a² - 81) = a² * (15)²
324 * (a² - 81) = a² * 225
324a² - 26244 = 225a²
324a² - 225a² = 26244
99a² = 26244
a² = 26244/99
a² = 265.1
a = √265.1
a = 16.3
