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a rectangular lawn has an area of 2,030 square meters. its perimeter is 198 meters. what are the dimensions of the lawn? show work

The dimension are 70  by 29

Step-by-step explanation:

The are of a rectangle is given as L X B , that means from the first statement , L X B = 2030

Also, the Perimeter of a rectangle is given by 2 ( L + B ), that means from the second statement 2 ( L + B ) = 198 , dividing this through by 2 , we have

L + B = 99

Combing the two equations, we have

LB = 2030 ........... 1

L + B = 99 ............ 2

Solving the resulting simultaneous equation

from equation 1 make L the subject , we have

L = 2030/B

Also, from equation 2 , make L the subject of the formula , we have

= 99 - B ............ **

Equate the two values of L , we have

2030 / B= 99 - B , by cross multiplying , we have

2030 = 99B -  

This is the same as   - 99B + 2030 = 0

This is a quadratic equation, solving by quadratic formula

L = 70 or 29

substituting this value into **

B = 29 or 70

Therefore the dimensions are 70 X29

step-by-step explanation:

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