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3 years ago

Area of a rectangle with a width of 36cm and a perimeter of 80cm

Mathematics

1 answer:

grandymaker [24]3 years ago

7 0

The area would be 144cm^2.

In order to find the area, we need to know the length of the rectangle. We can find that using the perimeter formula.

2l + 2w = P

2l + 2(36) = 80

2l + 72 = 80

2l = 8

l = 4

So now that we know the length is 4, we can find the area using that formula.

A = lw

A = (4)(36)

A = 144

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General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Functions
Function Notation

Algebra II

Piecewise Functions

Calculus

Limits
Continuity

Step-by-step explanation:

Step 1: Define

Identify

Continuous at x = 2

$\displaystyle f(x) = \left \{ {{2x^2 \ if \ x < 2} \atop {x + k \ if \ x \geq 2}} \right.$

Step 2: Solve for k

Definition of Continuity: $\displaystyle \lim_{x \to 2^+} 2x^2 = \lim_{x \to 2^-} x + k$
Evaluate limits: $\displaystyle 2(2)^2 = 2 + k$
Evaluate exponents: $\displaystyle 2(4) = 2 + k$
Multiply: $\displaystyle 8 = 2 + k$
[Subtraction Property of Equality] Subtract 2 on both sides: $\displaystyle 6 = k$
Rewrite: $\displaystyle k = 6$