Answer:
B) 8 cm
Step-by-step explanation:
Hello, I can help you with this
according to the question
The length of a rectangle is 3 cm greater than the width of the rectangle.
convert this into algebraic terms
Step 1
do the eqution
Let
W,width
L,Length
The length of a rectangle(L) is(=) 3 cm greater than the width (W+3) of the rectangle.
note:3 cm greater than the width (W+3) means that you need add 3 to the width to obtain the length
L=W+3 equation(1)
the area of the rectangle is 40 square cm
Let
A,Area
Area= 40 cm
A=40
also,A=L*W
40=L*W equation(2)
Step 2
solve the equations
L=W+3 equation(1)
40=L*W equation(2)
replace the value of L from equaiton (1) into equation (2)
[tex]40=(W+3)*W\\40=W^{2} +3W\\W^{2} +3W-40=0\\W^{2}+3W-40=0\\\\use cuadratic\\\\w=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}\\\\w=\frac{-3+-\sqrt{3^{2}-4*1*-40 } }{2*1}\\w=\frac{-3+-\sqrt{169} }{2}\\[/tex]
we are looking for a distance, so we need the positive valur only.
[tex]w=\frac{-3+-\sqrt{169} }{2}\\\\w=\frac{-3+13}{2}\\ w=5\\[/tex]
Step 3
Now, replace the value of W into equation (1) to obtain the length
L=W+3 equation(1)
L=5+3
L=8
so, the length is 8 cm, B) 8 cm
Have a nice day.
