Question

In a right-angled triangle the altitude to the hypotenuse is 8 cm high. The hypotenuse is 20 cm long. Find the lengths of the segements of the hypotenuse (Hint: let the length of the segment be x.)

In a right-angled triangle, the median to the hypotenuse is 6.4 cm. What is the length of the hypotenuse?

A bridge crosses a river at an angle of 60°. If the length of the bridge is 170 m, what is the width of the river?

If you deposit 6 500 FRW com-pounded monthly into an account paying 8% annual interest compounded monthly, how much money will be in the account after 7 years?

If you deposit 8 000 FRW into anaccount paying 7% annual interest  compounded quarterly, how long will it take to have 12 400 FRW in the account?

A car hire company with 24 cars uses 2 940 litres of petrol in 5 days. How long would 4 116 litres of petrol last if the company had 28 cars and the consumption rate does not change?

A new car falls in value by 30% a year. After a year, it is worth 84 000 FRW. Find the price of the car when it was new.            

Answer 1

1)

$$8=\sqrt{x(1-x)}20\\x=0.2\\a=0.2(20)=4\ cm\\b=0.8(20)=16\ cm$$

2)

$$c=2(6.4)=12.8\ cm$$

3)

$$c=170\cos{60}=85\ m$$

4)

$$6500\left(1+\frac{0.08}{12}\right)^{7\cdot12}=11358\ FRW$$

5)

$$8000\left(1+\frac{0.07}{4}\right)^{4t}=12400\\t=6.3\ years$$

6)

$$x=\frac{28}{24}\frac{4116}{2940}5=8.17\ days$$

7)

$$0.7x=84000\\x=120000\ FRW$$