SOLUTION: A rectangular lawn of length (x+5) metres is (x-2) metres wide. if the diagonal is (x+6) find the value of x and the area of the lawn?

Question 1054929: A rectangular lawn of length (x+5) metres is (x-2) metres wide. if the diagonal is (x+6) find the value of x and the area of the lawn?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Length,width,and diagonal of a rectangle are a right triangle with the diagonal the hypotenuse. The sum of the squares of the sides equals the square of the diagonal.
(x+5)^2+(x-2)^2=(x+6)^2
x^2+10x+25+x^2-4x+4=x^2+12x+36
2x^2+6x+29=x^2+12x+36
x^2-6x-7=0
(x-7)(x+1)=0
x=7; other route is not valid.
The triangle is a 5,12,13 triangle, units in meters.
The length is 12m, the width 5m, and the area 60 m^2.
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