Question

An altitude of the triangle is five third the lenght of its corresponding base. If the altitude is increased by 4cm and base be decreased by 2cm, the area of the triangle remains the same. Find the base and altitude of the triangle

Answer 1

see the image for the answer

Answer 2

Answer:

The base and altitude of the triangle is 12 cm and 20 cm respectively.

Step-by-step explanation:

Let the base be x

We are given that An altitude of the triangle is five third the length of its corresponding base.

Altitude = $\frac{5}{3}x$

Area of triangle = $\frac{1}{2} \times Base \times Height$

Area of triangle = $\frac{1}{2} \times x \times \frac{5}{3}x$

Area of triangle = $\frac{5}{6}x^2$

The altitude is increased by 4cm and base be decreased by 2cm

New Base = x-2

New Altitude = $\frac{5}{3}x+4$

Area of triangle = $\frac{1}{2} \times Base \times Height$

Area of triangle = $\frac{1}{2} \times (x-2) \times (\frac{5}{3}x+4)$

We are given that the area remain same

$\frac{1}{2} \times (x-2) \times (\frac{5}{3}x+4)=\frac{5}{6}x^2$

$x=12$

Base = 12 cm

Altitude = $\frac{5}{3}(12)=20 cm$

Hence the base and altitude of the triangle is 12 cm and 20 cm respectively.