Karen Morrison and Nick Hamshaw Solutions for Exercise 3: Exercise 22.3

The diagram given below shows a rectangle that has been divided into a square and a smaller rectangle.The smaller rectangle is similar to larger one.Solve the equation,$x^2-x-1=0$,giving the answer to $2$ decimal places.

The diagram given below shows a rectangle that has been divided into a square and a smaller rectangle.The smaller rectangle is similar to larger one.Solve the equation,$x^2-x-1=0$,giving the answer to $2$ decimal places.Explain why one of the solution does not work in this case.

The diagram given below shows a rectangle that has been divided into a square and a smaller rectangle.The smaller rectangle is similar to larger one.Solve the equation,$x^2-x-1=0$,giving the answer to $2$ decimal places.Find the perimeter of the rectangle.

The product of three consecutive integers is $30$ times smallest of the three integers.Find the two possible sets of integers that will satisfy this condition.

The square of a number is $14$ more than $5$ times the number. Find the two possible numbers for which this is true.​

A rectangle has sides of length $x cm$ and $y cm$. If the perimeter of the rectangle is $22 cm$ and the area of the rectangle is $24 c{m}^2$,use algebra to find the dimensions of the rectangle.

A ball is thrown from a building and falls $3t+5t^2 metres$ in $t sec.$ after how many seconds has the ball fallen $6 metre$ 

A stone is thrown up into the air from ground level. If the height of the stone is $16t-5t^2$, for how long will the stone be more than $8 m$ above the ground.