Rose Harrison and Clara Huizink Solutions for Exercise 21: Practice 7

A rectangular swimming pool measures $10 \mathrm{m}$ by $6 \mathrm{m}$. A paved area on two sides of the pool has width $x \mathrm{meters}$. The total area including the paved area is $\frac{4}{3}$ of the pool area on its own. Find $x$.

The perimeter of a rectangle is $42 \mathrm{cm}$. Its diagonal is $15 \mathrm{cm}$. Find the width of the rectangle in $\mathrm{cm}$.

A student cycles from home to school, due north for a distance $x \mathrm{km}$, then the same distance plus an additional $7 \mathrm{km}$ due east. If the direct distance from home to school is $17 \mathrm{km}$, find the distances that the student cycles north and east. 

A box has a square base of side $x \mathrm{cm}$, height $4 \mathrm{cm}$, and volume $289 {\mathrm{cm}}^3$. Find $x$.

Two numbers have a difference of $3$ and a product of $88$. Find the numbers.

The product of two consecutive odd numbers is $143$. Find the numbers.

The sum of the two numbers is $9$ and the sum of their squares is $153$. Find the two numbers.

When the square of a number is decreased by $1$, the result is $4$ times the original number. Find the number.