A rectangular field is 90 meters wide and 125 meters long. Give the length and width of another rectangular field that has the same perimeter but a larger area.

The length and the width of another rectangle are 115 meters and 100 meters

Step-by-step explanation:

Let us solve the question

∵ A rectangular field is 90 meters wide and 125 meters long

∴ The length = 125 m

∴ The width = 90 m

∵ The perimeter of the rectangle = 2(length + width)

→ Substitute the value of the length and the width in the rule

∴ The perimeter of the rectangle = 2(125 + 90)

∴ The perimeter of the rectangle = 430 m

∵ The area of the rectangle = length × width

→ Substitute the value of the length and the width in the rule

∴ The area of the rectangle = 125 x 90

∴The area of the rectangle = 11250 m²

We need to find another rectangle with the same perimeter but larger in area, to do that make the length and width closed in values

∵ The length = 125 m and the width = 90 m

→ Subtract 10 from the length and add it to the width

∴ The new length = 125 - 10 = 115 m

∴ The new width = 90 + 10 = 100 m

→ Find the perimeter and the area of the new rectangle

∵ The perimeter of the new rectangle = 2(115 + 100)

∴ The perimeter of the new rectangle = 430 m ⇒ the same perimeter

∵ The area of the new rectangle = 115 × 100

∴ The area of the new rectangle = 11500 m² ⇒ larger than the original area

∴ The length and the width of another rectangle are 115 m and 100 m

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: