Area of a triangle is given by the formula a=1/2 bh. the area of the triangle shown to the right is 56 sq. units. find its base and height

read the problem carefully. to find the base and height, first identify the base and the height from the given figure.

for the given triangle, the base is and the height

Given

base=2x+6
height=x+4

and
area=56 square units

56=1/2 times (2x+6) times (x+4)
times bot sides by 2
112=(2x+6)(x+4)
expand
112=2x²+14x+24
divide both sides by 2
56=x²+7x+12
minus 56 both sides
0=x²+7x-44
factor
waht 2 numbers mulitply to get -44 and add to get 7
11 and -4
0=(x-4)(x+11)
set to 0

x-4=0
x=4

x+11=0
x=-11
false, measures can't be negative

x=4

height=x+4
height=4+4=8

base=2x+6
base=2(4)+6=8+6=14

x=4 and base=14 and height=8

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. if you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.