Answer:
Step-by-step explanation:
<h3><u>Answer</u><u>:</u></h3>
<h3><u>Solution</u><u>:</u></h3>
<em>We are given that :</em>
- A semicircle is drawn onto the shorter side of rectangle.
- Shorter side of rectangle measures 4cm. i.e; the diameter of the circle is 4cm
- Area of the figure is 41.4 cm²
<em><u>Using </u><u>Formulas</u><u>:</u></em>
Area of rectangle:
![\quad\hookrightarrow\quad{\pmb{ \mathfrak {length\times breadth }}}](https://tex.z-dn.net/?f=%20%5Cquad%5Chookrightarrow%5Cquad%7B%5Cpmb%7B%20%5Cmathfrak%20%7Blength%5Ctimes%20breadth%20%7D%7D%7D)
Area of semicircle:
![\quad\hookrightarrow\quad{\pmb{ \mathfrak{ \dfrac{\pi r^2 }{2}}}}](https://tex.z-dn.net/?f=%20%5Cquad%5Chookrightarrow%5Cquad%7B%5Cpmb%7B%20%5Cmathfrak%7B%20%5Cdfrac%7B%5Cpi%20r%5E2%20%7D%7B2%7D%7D%7D%7D)
- <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>length </u><u>of </u><u>longer </u><u>side </u><u>of </u><u>rectangle</u><u>!</u>
Here, we can know that the figure is composed of one rectangle and one semicircle. Therefore by combining the areas of rectangle and circle and taking the length of rectangle as a variable , we will finds its value ;
![\quad\dashrightarrow\quad \sf {Area_{\tiny { total}} = Area_{\tiny {rectangle}}+ Area_{\tiny {semicircle}}}](https://tex.z-dn.net/?f=%20%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7BArea_%7B%5Ctiny%20%7B%20total%7D%7D%20%3D%20Area_%7B%5Ctiny%20%7Brectangle%7D%7D%2B%20Area_%7B%5Ctiny%20%7Bsemicircle%7D%7D%7D)
![\quad\dashrightarrow\quad \sf {A = ( l \times b ) + \dfrac{\pi r^2 }{2} }](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7BA%20%3D%20%28%20l%20%5Ctimes%20b%20%29%20%2B%20%5Cdfrac%7B%5Cpi%20r%5E2%20%7D%7B2%7D%20%7D)
![\quad\dashrightarrow\quad \sf {41.4 = ( l \times 4 ) +\dfrac{3.14\times 2^2}{2} }](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7B41.4%20%3D%20%20%28%20l%20%5Ctimes%204%20%29%20%2B%5Cdfrac%7B3.14%5Ctimes%202%5E2%7D%7B2%7D%20%7D)
![\quad\dashrightarrow\quad \sf { 41.4= ( l \times 4 )+ \dfrac{ 3.14\times 4}{2}}](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7B%2041.4%3D%20%28%20l%20%5Ctimes%204%20%29%2B%20%5Cdfrac%7B%203.14%5Ctimes%204%7D%7B2%7D%7D)
![\quad\dashrightarrow\quad \sf { 41.4=( l \times 4 )+ \dfrac{12.56}{2}}](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7B%2041.4%3D%28%20l%20%5Ctimes%204%20%29%2B%20%5Cdfrac%7B12.56%7D%7B2%7D%7D)
![\quad\dashrightarrow\quad \sf { 41.4= (l \times 4 )+ 6.28}](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7B%2041.4%3D%20%28l%20%5Ctimes%204%20%29%2B%206.28%7D)
![\quad\dashrightarrow\quad \sf {l \times 4 = 41.4-6.28 }](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7Bl%20%5Ctimes%204%20%3D%2041.4-6.28%20%7D)
![\quad\dashrightarrow\quad \sf { l\times 4 = 35.12}](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7B%20l%5Ctimes%204%20%3D%2035.12%7D)
![\quad\dashrightarrow\quad \sf { l =\dfrac{35.12}{4}}](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Csf%20%7B%20l%20%3D%5Cdfrac%7B35.12%7D%7B4%7D%7D)
![\quad\dashrightarrow\quad \underline{\underline{\pmb{\sf {l = 8.78\:cm}}} }](https://tex.z-dn.net/?f=%20%5Cquad%5Cdashrightarrow%5Cquad%20%5Cunderline%7B%5Cunderline%7B%5Cpmb%7B%5Csf%20%7Bl%20%3D%208.78%5C%3Acm%7D%7D%7D%20%7D)
Answer: a=-1
Step-by-step explanation:
Answer:
9%
Step-by-step explanation:
Let the required number be 100.
Now, according to the question, the number is first increased by 30 %
⇒ 100 + 30 % of 100
⇒ 100 + [(30*100)/100]
⇒ 100 + 30
⇒ 130
Then, it is decreased by 30 %
⇒ 130 - (30 % of 130)
⇒ 130 - [(30*130)/100]
⇒ 130 - 39
⇒ 91
Net Decrease = 100 - 91
= 9
Percent Decrease = (Change in number*100)/100
⇒ (9*100)/100
= 9 %