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PLEASE HELP ! The height of a triangle is 4 feet greater than the base. The area of the triangle is 142.5 square feet. Find the length of the base and the height of the triangle

Sagot :

danielgeyfman

Answer:

Base: [tex]15[/tex], Height: [tex]19[/tex]

Step-by-step explanation:

Let the base be [tex]b[/tex]. Then the height is [tex]b+4[/tex].

By the area of a triangle theorem, we have that [tex]bh/2=b(b+4)/2=142.5[/tex].

Multiplying by [tex]2[/tex] and expanding gives [tex]b^2+4b=285[/tex], so [tex]b^2+4b-285=0[/tex]. We see that this quadratic factors into [tex](b-15)(b+19)=0[/tex]. Because the base is a side length and must be positive, we have that the base is [tex]15[/tex].

The height is then [tex]15+4=19[/tex].

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