Question

The base of atriangle is 4cm longer than its altitude. If the area of the triangle is 48sq.cm then find its base and altitude in telugu medium

Answer 1

Answer:

base = 12 cm

altitude = 8 cm

Step-by-step explanation:

area of triangle = 1/2 × base × altitude = 48 sq cm

let the altitude be x

the base is 4 cm more than altitude = x + 4

area = 48 sq cm

$48 = \frac{1}{2} (x \times (x + 4)) \\ 48 \times 2 = {x}^{2} + 4x \\ 96 = {x}^{2} + 4x \\ {x}^{2} + 4x - 96 = 0 \\ {x}^{2} + 12x - 8x - 96 = 0 \\ x(x + 12) - 8(x + 12) = 0 \\ (x + 12)(x - 8) = 0 \\ x + 12 = 0 \: \: \: \: \: \: \: x - 8 = 0 \\ x = - 12 \: \: \: \: \: \: \: \: \: \: \: x = 8$

as length can not be in negative we take x = 8

therefore the altitude = x = 8 cm

base = x + 4 = 8 + 4 = 12 cm

Hope you get your answer