Question

the length of a rectangular painting is 3 inches longer than its width. if the diagonal is 15 inches long, what is the length of the painting?
a. 9 inches
b. 12 inches
c. 13 inches
d. 18 inches
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Define variables for width/length

Let width $w = x$, length $l = x+3$

Step2: Apply Pythagorean theorem

$$x^2 + (x+3)^2 = 15^2$$

Step3: Expand and simplify equation

$$x^2 + x^2 +6x +9 = 225$$
$$2x^2 +6x -216 =0$$
$$x^2 +3x -108=0$$

Step4: Solve quadratic equation

Factor: $(x+12)(x-9)=0$
Solutions: $x=9$ or $x=-12$ (discard negative)

Step5: Calculate length

Length $= 9+3=12$ inches

Answer:

B. 12 inches