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KonstantinChe [14]
2 years ago
6

The area of a parallelogram is 3.36 square feet. the base is 2.8 feet. if the measures of the base and height are each doubled,

find the area of the resulting parallelogram
Mathematics
1 answer:
kolbaska11 [484]2 years ago
5 0
A =bh

Plug in values and solve for height (h).
A=3.36
b=2.8

3.36 = 2.8h
/2.8      /2.8
1.2 = h

Base and Height doubled:
b = 2.8
h = 1.2

2(2.8)=5.6
2(1.2)=2.4

Plug in new b and h to area equation given to find area:
5.6(2.4) = 13.44

Resulting parallelogram area = 13.44 ft^2
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\bold{\huge{\green{\underline{ Solution }}}}

\bold{\underline{ Given}}

  • <u>We </u><u>have </u><u>given </u><u>that </u><u>the </u><u>coordinates </u><u>of </u><u>the </u><u>end </u><u>point </u><u>G </u><u>and </u><u>H </u><u>are </u><u>(</u><u> </u><u>-</u><u>6</u><u>,</u><u>5</u><u>)</u><u> </u><u>and </u><u>(</u><u> </u><u>2</u><u>,</u><u> </u><u>-</u><u>7</u><u> </u><u>)</u>

\bold{\underline{To  \: Find :- }}

  • <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>length </u><u>of </u><u>GH </u>

\bold{\underline{Let's \:  Begin :- }}

The coordinates of G = ( -6 , 5 )

The coordinates of H = ( 2 , - 7 )

<u>According </u><u>to </u><u>the </u><u>distance </u><u>formula</u><u>, </u><u> </u><u>we </u><u>get </u><u>:</u><u>-</u><u> </u>

\purple{\bigstar}\boxed{\sf{Distance\:\:GH=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}

  • <u>Here</u><u>, </u><u> </u><u>x1</u><u> </u><u>=</u><u> </u><u>-</u><u>6</u><u> </u><u>,</u><u> </u><u>x2</u><u> </u><u>=</u><u> </u><u>2</u><u> </u><u>and </u><u>y1</u><u> </u><u>=</u><u> </u><u>5</u><u> </u><u>,</u><u> </u><u>y2</u><u> </u><u>=</u><u> </u><u>-</u><u>7</u>

<u>Subsitute </u><u>the </u><u>required </u><u>values </u><u>in </u><u>the </u><u>above </u><u>formula </u>

\sf{ Distance \:GH = √( -6 - 2)² + ( 5 -(-7))²}

\sf{Distance\:GH= √(-8)^2+(5 + 7)^2}

\sf{Distance\:GH=√(-8)^2+(12)^2}

\sf{ Distance \:GH =√64 + 144 }

\sf{ Distance \:GH =√ 208}

\sf{ Distance\: GH = √ 2 × 2 × 2 × 2 × 13}

\sf{ Distance \:GH = 4√13}

\sf{\red{ Hence\: the \: length\:of \: GH \: is \: 4√13 \: units}}

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