The lengths of the sides are in centimetres.

The area of triangle ${T}_{1}$ is equal to the area of triangle ${T}_{2}$.
Work out the value of $x$, giving your answer in the form $a+\sqrt{b}$ where $a$ and $b$ are integers.

The diagram shows a rectangle, $ABDE$ , and two congruent triangles, $AFE$and $BCD$.

area of rectangle $ABDE$ = area of triangle $AFE$ + area of triangle $BCD$

$AB:AE=1:3$

Work out the length of $AE$.

.....................................cm

A sphere has radius $2xcm$

A cone has

   radius $3xcm$    
perpendicular height $hcm$

The sphere and the cone have the same volume.

Work out    radius of cone : perpendicular height of cone

Give your answer in the form $a:b$where $a$ and $b$ are integers.

The diagram shows a sector $OBC$ of a circle with centre $O$ and radius $(6+x)cm$.

$A$ is the point on $OB$ and $D$ is the point on $OC$ such that $OA=OD=6cm$

Angle $BOC=50^{\circ}$

Given that

the perimeter of sector $OBC=2\times$the perimeter of triangle $OAD$

find the value of $x$.

Give your answer correct to 3 significant figures.