(g) A house owner wants to build an extension in the shape of a cuboid so that the length l is 3 m longer than the width. Find l in terms of w.
Rectangle Q has length (x + 4) and breadth 4.
Q x + 4 w l
The planning regulations state that the area of the fl oor space occupied by the extension must not exceed 50% of the fl oor space of the house to which it is attached. The fl oor space of the house is 14 m by 12 m. Show that w 2 + 3w – 84 = 0, if the largest extension is built. Find l and w, correct to one decimal place.
(h) Rectangle P has length (x + 10) and breadth x.
Px x + 10 P x Q
Find x if the rectangles have the same area.
(i) In a right-angled triangle, the length of [PR] is 7 cm longer than [PQ]. The length of the hypotenuse is 8 cm longer than [PQ]. Find the lengths of all sides.
