The length of the base of a triangle is twice its height. if the area of the triangle is 196 square kilometers, find the height.

Area = 1/2 x base x height

Let the height be x.
Height = x
Base = 2x

Area of triangle = 1/2 x base x  heght

Plug base and height into the variables:
(1/2)(2x)(x) = 196

Combine like terms:
x² = 196

Square root both sides:
x = 14

Find Base and height:
Base = x = 14 km
Height = 2x = 2(14) = 28 km

Height = 28km

Hey user!

your answer is here..

ATQ,

the length of the base of the triangle is twice it's height.

let the height of the triangle be x.

therefore base of the triangle is 2x.

given area of the triangle = 196km²

==> 1/2 × b × h = 196km²

==> 1/2 × 2x × x = 196km²

==> x × x = 196km²

==> x² = 196km²

==> x = √196

==> x = 14

hence, height of the triangle = x = 14km

base of the triangle = 2x = 2 × 14 = 28km

VERIFICATION :-

area of the triangle = 1/2 × b × h

= 1/2 × 14 × 28

= 7 × 28

= 196km²

hence verified..

cheers!!