Question

. You are making a frame of uniform width for a picture that is to be displayed at the local museum. The picture is 4 feet tall and 3 feet wide. The museum has allcoated 30 square feet of wall space to display the picture. What should the width of the frame be in order to use all of the allocated space?

Answer 1

Answer:

1 feet

Explanation:

Frame width = x

The length of the frame will be

$L=4+x+x$ (bottom and top that is why x is added twice)

$\\\Rightarrow L=4+2x$

The width of the frame will be

$W=3+x+x\\\Rightarrow W=3+2x$

Area is given by

$A=LW\\\Rightarrow 30=(4+2x)(3+2x)\\\Rightarrow 30=12+14x+4x^2\\\Rightarrow 4x^+14x-18=0$

Solving the above equation we get

$x=\frac{-14+\sqrt{14^2-4\cdot \:4\left(-18\right)}}{2\cdot \:4}, \frac{-14-\sqrt{14^2-4\cdot \:4\left(-18\right)}}{2\cdot \:4}\\\Rightarrow x=1, -\frac{9}{2}$

Hence width of the frame is 1 ft