Chapter 8, Problem 26PT

To determine

The formula $A=\frac{1}{2}{d}_1{d}_2$ for the variabledℹ

Answer to Problem 26PT

  $d_2=\frac{2A}{d_1}$

Explanation of Solution

Given information:

A formula for the area of the kite is $A=\frac{1}{2}{d}_1{d}_2$ and dℹd ℹ represent the length of the diagonals.

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve for the variable dℹ, first multiply both sides by 2 and then divide both sides by d 1 to simplify further as shown below:

  $\begin{array}{l}A=\frac{1}{2}{d}_1{d}_2\\ 2\times A=2\times \frac{1}{2}{d}_1{d}_2\\ 2A=d_1{d}_2\\ \frac{2A}{d_1}=\frac{d_1{d}_2}{d_1}\\ \frac{2A}{d_1}=d_2\\ d_2=\frac{2A}{d_1}\end{array}$

Thus, the formula for the variable is $d_2=\frac{2A}{d_1}$ .