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

Answer:

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

Step-by-step explanation:

we know that

The area of triangle is equal to

$A=\frac{1}{2}bh$ ----> equation A

where

b is the base and h is the height

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

substitute equation B in equation a

$A=\frac{1}{2}b(2b+2)$

we have that

$A=56\ cm^2$

so

$56=\frac{1}{2}b(2b+2)$

$112=2b^2+2b$

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

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