Get personalized answers to your unique questions on IDNLearn.com. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.
Sagot :
Given
The base and height of a parallelogram is (x-7)meters and (x+9)meters respectively.
[tex]\begin{gathered} \text{Base(b) = (x-7)meters} \\ Height=\text{ (x+9)meters} \end{gathered}[/tex]Formula
[tex]\begin{gathered} \text{The area of a Paralelogram = Base}\times Height \\ \end{gathered}[/tex][tex]\text{The area is 192m}^2[/tex]We now substitute into the formula
[tex]\begin{gathered} 192=\mleft(x-7\mright)\mleft(x+9\mright) \\ 192=x^2+9x-7x-63 \\ 192=x^2+2x-63 \\ \text{REARRANGE} \\ x^2+2x-63-192=0 \\ x^2+2x-255=0 \\ \end{gathered}[/tex]It is now Quadratic Equation
[tex]\begin{gathered} a=1,\text{ b=2 and c=-255} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ We\text{ can now substitute into the quadratic formula} \\ x=\frac{-2\pm\sqrt[]{2^2^{}-4\times1\times-255}}{2\times1} \\ \\ x=\frac{-2\pm\sqrt[]{4^{}--1020}}{2} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{1024}}{2} \\ \\ x=\frac{-2\pm32}{2} \\ \\ x=\frac{-2+32}{2}=\frac{30}{2}=15 \\ \\ or \\ x=\frac{-2-32}{2}=-\frac{34}{2}=-17 \end{gathered}[/tex]For distance or dimension it can't be negative, so we choose the positive
x=15
Recall from the question
Base=(x-7)meters
Height= (x+9)meters
We can now replace x with 15
[tex]\begin{gathered} \text{Base}=\text{ 15-7} \\ \text{Base}=8m \\ \\ \text{Height =15+9} \\ \text{Height}=24m \end{gathered}[/tex]The final answer
Base is 8m
Height is 24m
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.
