Question

"No passing zone" sign has the shape of an isosceles triangle. The width of the sign is 7 inches greater than it's height. The top and bottom edges of the sign are 44 inches
A) use the Pythagorean theorem to write an equation that relates X, 2x+7 and 44. (Leave fractions, not decimals, in your answer).
B) solve the equation by completing the square
C) what is the height of the sign?

Answer 1

A) $x^{2} + (2x + 7)^{2} = 44^{2}$

B) $5x^{2} + 28x + 49 = 1936$

$$x^{2} + \frac{28}{5}x = \frac{1887}{5}$$ $$x^{2} + \frac{28}{5}x + \frac{196}{25} = \frac{1887}{5} + \frac{196}{25}$$ $$(x + \frac{14}{5})^{2} = \frac{1887 \times 5 + 196}{25} = \frac{9631}{25}$$ $$(x + \frac{14}{5}) = \pm \frac{98}{5}$$

x can not be negative, so $x = \frac{84}{5} \approx 16$ inches

C) height is 32 inches