Question

1. the height of a rectangle is 3 less than twice its base, b. the perimeter of this rectangle is

. use algebra to determine the length of the base of this rectangle, b.

Explanation:

Step1: Express height in terms of base

The height $h$ of the rectangle is 3 less than twice its base $b$, so $h = 2b-3$.

Step2: Write perimeter formula

The perimeter $P$ of a rectangle is $P=2(b + h)$. Given $P = 34$ (assuming the perimeter value is 34 as it's missing in the problem - if it's another value, the following steps can be adjusted accordingly), we substitute $h = 2b - 3$ into the perimeter formula: $34=2(b+(2b - 3))$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $34=2(b + 2b-3)=2(3b - 3)$. Then distribute the 2: $34 = 6b-6$.

Step4: Solve for b

Add 6 to both sides of the equation: $34 + 6=6b-6 + 6$, which gives $40 = 6b$. Then divide both sides by 6: $b=\frac{40}{6}=\frac{20}{3}$.

Answer:

$b=\frac{20}{3}$