Question

1. What must be the dimensions of a rectangle to have an area 125m^2 and a perimeter of 60m?

2. In a right angle the hypotenuse is 15cm. if the second side is twice the length of the third side, calculate the exact length pf the shortest side.

3. THe height h metres of a cricket ball after being struck by a batsman is given by the equation h = 1 + x - x^2/40 where x metres is the horizontal distance travelled by the ball from the bat. How far would the ball travel before it hits the ground?

Answer 1

#1 You need to solve
2(x+y) = 60
xy = 125
so, since y=30-x,
x(30-x) = 125
x = 5 or 25

#2 It sounds like you want x where
x^2 + (2x)^2 = 15^2

#3 it hits the ground when its height is zero, so you need to solve
-x^2/40+x+1 = 0
making it a bit more comfortable by clearing fractions and having a positive leading coefficient, solve
x^2 - 40x - 40 = 0