The width of a rectangular window is 2 feet more than its height. If the area is 35 square feet, what is the height of the window?
Answer (3)
0\ then\ h_1=\frac{-b-\sqrt\Delta}{2a}\ and\ h_2=\frac{-b+\sqrt\Delta}{2a}\\\\\Delta=2^2-4\cdot1\cdot(-35)=4+140=144;\ \sqrt\Delta=\sqrt{144}=12\\\\h_1=\frac{-2-12}{2\cdot1}=\frac{-14}{2}=-7 < 0;\ h_2=\frac{-2+12}{2\cdot1}=\frac{10}{2}=5\\\\Answer:Height\ is\ 5\ ft."> h − h e i g h t h + 2 − w i d t h 35 f t 2 − A re a A re a = h ( h + 2 ) h ( h + 2 ) = 35 h 2 + 2 h − 35 = 0 a = 1 ; b = 2 ; c = − 35 Δ = b 2 − 4 a c ; i f Δ > 0 t h e n h 1 = 2 a − b − Δ an d h 2 = 2 a − b + Δ Δ = 2 2 − 4 ⋅ 1 ⋅ ( − 35 ) = 4 + 140 = 144 ; Δ = 144 = 12 h 1 = 2 ⋅ 1 − 2 − 12 = 2 − 14 = − 7 < 0 ; h 2 = 2 ⋅ 1 − 2 + 12 = 2 10 = 5 A n s w er : He i g h t i s 5 f t .
To find the height of the rectangular window, set up an equation using the given information and solve for the height, which is 5 feet. ;
The height of the rectangular window is 5 feet, derived from setting up the area equation and solving a quadratic equation. The window's width is 2 feet more than its height. Therefore, by using the quadratic formula, we confirmed that the only valid height is 5 feet.
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