How do you find the perimeter and area of a rectangle with width of 2sqrt7-2sqrt5 and length of 3sqrt7+3sqrt5?

4 Answers
May 18, 2017

Perimeter P = 10 sqrt(7) + 2 sqrt(5)

Area A = 12

Explanation:

The perimeter P of a rectangle is the sum of all side lengths.

The formula is P = 2(l + w), where l is the length and w is the width:

Rightarrow P = 2((3 sqrt(7) + 3 sqrt(5)) + (2 sqrt(7) - 2 sqrt(5)))

Rightarrow P = 2(3 sqrt(7) + 2 sqrt(7) + 3 sqrt(5) - 2 sqrt(5))

Rightarrow P = 2(5 sqrt(7) + sqrt(5))

therefore P = 10 sqrt(7) + 2 sqrt(5)

The area A of a rectangle is the product of the length and the width.

The formula is A = l w:

Rightarrow A = (3 sqrt(7) + 3 sqrt(5)) times (2 sqrt(7) - 2 sqrt(5))

Rightarrow A = 3 sqrt (7) times 2 sqrt(7) + 3 sqrt(7) times (- 2 sqrt(5)) + 3 sqrt(5) times 2 sqrt(7) + 3 sqrt(5) times (- 2 sqrt(5))

Rightarrow A = 6 times 7 - 6 sqrt(35) + 6 sqrt(35) - 6 times 5

Rightarrow A = 42 - 30

therefore A = 12

Therefore, the perimeter is 10 sqrt(7) + 2 sqrt(5) and the area is 12.

May 18, 2017

Perimeter of rectangle is 2(5sqrt 7+sqrt5) unit.

Area of rectangle is 12 sq.unit.

Explanation:

Length of rectangle is l= 3 sqrt7 +3 sqrt 5
Width of rectangle is w= 2 sqrt7 -2 sqrt 5

Perimeter of rectangle is P=2l+ 2w = 2(3 sqrt7 +3 sqrt 5) +2(2 sqrt7 -2 sqrt 5)

P= sqrt7(6+4) + sqrt5 (6-4) = 10sqrt 7 +2sqrt5 =2(5sqrt 7+sqrt5)unit

Area of rectangle is A= l*w= (3 sqrt7 +3 sqrt 5)*(2 sqrt7 -2 sqrt 5)

A= 6 * 7 - cancel(6 * sqrt 35) + cancel(6 sqrt35) -6*5 = 42-30 =12 sq.unit.

Perimeter of rectangle is 2(5sqrt 7+sqrt5) unit
Area of rectangle is 12 sq.unit. [Ans]

May 18, 2017

12

Explanation:

we know area of rectangle = length*width sq unit.

So, color(green)(Area) = [3sqrt7 +3sqrt5]xx[2sqrt7-2sqrt5]

rArr 3[sqrt7+sqrt5]xx2[sqrt7-sqrt5]

rArr 3xx2xx[(sqrt7)^2-(sqrt5)^2]

rArr 3xx2xx[7-5] = 3xx2xx2 =12 sq unit

color(red)(perimeter)= 2*[length+width]unit

rArr 2[{3sqrt7+3sqrt5}+{2sqrt7-2sqrt5}]

rArr2[3sqrt7+3sqrt5+2sqrt7-2sqrt5]

rArr2[5sqrt7+sqrt5]

May 18, 2017

Areacolor(blue)(=12 color(white)(a)square units,color(blue)(P=2(5sqrt7+sqrt5)

Explanation:

W=2sqrt7-2sqrt5

L=3sqrt7+3sqrt5

perimeter of a rectangle=P=L+W+L+W

P=2L+2W=2(L+W)

P=2[(3sqrt7+3sqrt5)+(2sqrt7-2sqrt5)]

P=2[3sqrt7+3sqrt5+2sqrt7-2sqrt5]

P=2[5sqrt7+sqrt5]

Area=A=W xx L

A=(2sqrt7-2sqrt5) xx (3sqrt7+3sqrt5)

color(white)(aaaaaaaaaaaaa)2sqrt7-2sqrt5
color(white)(aaaaaaaaaa) xx underline(3sqrt7+3sqrt5)
color(white)(aaaaaaaaaaaaa)6 xx 7-6sqrt5sqrt7
color(white)(aaaaaaaaaaaaaaaaaaaa)6sqrt5sqrt7-6 xx 5
color(white)(aaaaaaaaaaaaaa)overline(42-30color(blue)(=12 square units