Question

The length of a rectangle is 3 cm greater than the width of the rectangle.

Answer 1

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)

$40=(W+3)*W\\40=W^{2} +3W\\W^{2} +3W-40=0\\W^{2}+3W-40=0\\\\use cuadratic\\\\w=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}\\\\w=\frac{-3+-\sqrt{3^{2}-4*1*-40 } }{2*1}\\w=\frac{-3+-\sqrt{169} }{2}$

we are looking for a distance, so we need the positive valur only.

$w=\frac{-3+-\sqrt{169} }{2}\\\\w=\frac{-3+13}{2}\\ w=5$

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.