Q:

Find the area of a triangle with a=20, b=30, and c=40A.)400.5 units^2B.)364.0 units^2C.)290.5 units^2D.)284.25 units^2

Accepted Solution

A:
Answer:option C is correct.Step-by-step explanation:The area of triangle with sides a, b and c can be found by using formula[tex]Area = \sqrt{s(s-a)(s-b)(s-c)} \\where \\s= \frac{1}{2}(a+b+c)[/tex]We are given:a= 20b=30c=40Finding s:Putting values in the formula and solving:[tex]s= \frac{1}{2}(a+b+c)\\s=\frac{1}{2}(20+30+40)\\s=\frac{90}{2}\\s= 45[/tex]Now, Finding the area:Putting values in the formula and solving:[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}\\Area =\sqrt{45(45-20)(45-30)(45-40)}\\Area =\sqrt{45(25)(15)(5)}\\Area = \sqrt{84,375} Β \\Area = 290.5 units^2[/tex]So, option C 290.5 units^2 is correct.