Question

In the figure above, square ABCD and triangle EFG have the same areas. If AB =6 and EG =8, what is the height o triangle EFG?

Answer 1

Answer:

The height of triangle EFG is 9 units

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the area of a square ABCD

The area of a square is equal to

$A=b^2$

where

b is the length side of the square

we have

$b=AB=6\ units$

substitute

$A=6^2=36\ units^2$

step 2

Find the height of triangle EFG

The area of triangle EFG is equal to

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

where

b is the base of triangle

h is the height of triangle

we have

$b=EG=8\ units$

$A=36\ units^2$ ---> area of triangle EFG is the same that the area of square ABCD

substitute the given values in the formula

$36=\frac{1}{2}(8)(h)$

solve for h

$36=4h\\h=9\ units$

therefore

The height of triangle EFG is 9 units