Question

An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude
increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains the
same. Find the base and the altitude of the triangle.​

Answer 1

Answer:

Height = 20 cm

Base = 12 cm

Step-by-step explanation:

Given, $h = \frac{5b}{3}$  where h is height and b is base of triangle.

So area is $\frac{1}{2} (b\frac{5b}{3} )  = \frac{5b^2}{6}$

Also given that at height of (h+4) and base at (b-2) the area is same.

So  $\frac{1}{2} (b\frac{5b}{3} + 4 )(b-2) = [tex]\frac{5b+12}{3} (b-2) = \frac{5b^2}{6}\\5b^{2} - 10b +12b - 24 = 3b^2\\2b = 24\\b = 12$

So height h = $\frac{5(12)}{3}  = \frac{60}{3}  = 20 cm$