Question

The area of a triangular flag is 56 square centimeters. It’s altitude is 2 centimeters longer than twice it’s bases find the length of the altitude and the base

Answer 1

The length of the altitude is 16 centimeters and the base is 7 centimeters

Explanation:

we know that

The area of triangle is equal to

`A=(1)/(2)bh` ----> equation A

where

b is the base and h is the height

`h=2b+2` ----> equation B

substitute equation B in equation a

`A=(1)/(2)b(2b+2)`

we have that

`A=56\ cm^2`

so

`56=(1)/(2)b(2b+2)`

`112=2b^2+2b`

`2b^2+2b-112=0`

solve the quadratic equation by graphing

the solution is b=7 cm

see the attached figure

Find the value of h

`h=2(7)+2=16\ cm`

therefore

The length of the altitude is 16 centimeters and the base is 7 centimeters