Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

2. The height of a triangle is 5 m less than its base. The area of the triangle is 42 m2. Find the length of the base.
(Points : 1)


Sagot :

ddk
Let's start with what we know

Area:
[tex]42 = \frac{1}{2}bh [/tex] where 42 is the area, b = base, and h = height

Height:
Since we know the height is 5 less than the base, we can write that as an equation.
[tex]h = b - 5[/tex]

Now let's go and plug [tex]h = b - 5[/tex] into [tex]42 = \frac{1}{2}bh [/tex]

[tex]42 = \frac{b}{2}(b-5)[/tex]
Let's distribute b over (b-5)

[tex]42 = \frac{ b^{2} - 5b }{2}[/tex]
Let's move 42 over to the right side to make a quadratic formula

[tex]0 = \frac{1}{2} b^{2} - \frac{5}{2}b - 42[/tex]

Let's plug that into the quadratic equation, which is:

[tex] \frac{-b +/- \sqrt{ b^{2} - 4ac } }{2a} [/tex]
And we can now plug the pieces in to calculate b

[tex] \frac{- (-\frac{5}{2}) +/- \sqrt{ (-\frac{5}{2})^{2} - 4 (\frac{1}{2})(-42) } }{2 (\frac{1}{2}) } [/tex]
[tex] \frac{\frac{5}{2} +/- \sqrt{ \frac{25}{4} +84 } }{1 } [/tex]
[tex]{\frac{5}{2} +/- \sqrt{ \frac{361}{4} } }[/tex]
[tex]{\frac{5}{2} +/- { \frac{19}{2} } [/tex]
Since we can't have a negative value for b (a base can't be negative meters), let's add:

[tex]{\frac{5}{2} + { \frac{19}{2} } [/tex]
[tex]{ \frac{24}{2} } [/tex]
[tex]12 = b[/tex]

So the base of the triangle is 12m

Answer:

took the quiz and it is correct the answer is 12

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.