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The base of a triangle exceeds the height by 4 feet. If the area is 58.5 square feet, find the length of the base and the height of the triangle.

Sagot :

towl35

Answer:

The answer is the height h equals 9

Step-by-step explanation:

[tex]a = \frac{1}{2} bh = 58.5\\ b = h + 4[/tex]

[tex]58.5 = \frac{(h + 4)h}{2} = \frac{ {h}^{2} + 4h}{2} [/tex]

[tex]117 = {h}^{2} + 4h \\ {h}^{2} + 4h - 117 = 0[/tex]

[tex] x1 = - 2 + u \\ x2 = - 2 - u\\ x1x2 = ( - 2 + u)( - 2 - u) = - 117[/tex]

[tex]4 - {u}^{2} = - 117 \\ 4 + 117 = {u}^{2} \\ {u}^{2} = 121[/tex]

[tex] \sqrt{ {u}^{2} } = + or - \sqrt{121} \\ u = + or - 11[/tex]

[tex]x1 = - 2 + 11 = 9 \: or \\ x2 = - 2 - 11 = - 13[/tex]

since areas have to be positive -13 is incorrect therefore

[tex]h = 9[/tex]

Check:

[tex]58.5 = \frac{(h + 4)h}{2} = \frac{(9 + 4)9}{2} = \\ \frac{13 \times 9}{2} = \frac{117}{2} = 58.5[/tex]

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