Question

A rectangle lawn of length +x+5) metre is (x--2) metre wide if the diagonal is +x+6 metres wide find I the value of the lawn ii the area of the lawn

Answer 1

(x+5)^2 + (x-2)^2 = (x+6)^2
x^2 + 10 x + 25 + x^2 - 4 x + 4 = x^2 + 12 x +36
x^2 - 6 x - 7 = 0
(x-7)(x+1) = 0
x = 7 ...... (or -1 but that does not work :)
Length = 7 + 5 = 12 meters
width = 7-2 = 5 meters
area = 5 * 12 = 60 meters^2

Answer 2

the solution seems wrong because of the square or the two that is being used to expand the bracket it has to be 2x + 10 2x - 4

Answer 3

(X+5)²+(X-2)²= (x+6)²
x²+10x+25+x²-4x+4-x²-12x-36=0
x²-6x-7=0
(x-7)(X+1)=0
X=7(negative not acceptable)
the value of X is 7
b). Area=length × width
A=(7+5) (7-2)
=(12)(5)
=60
Area is equal to 60 metres