# 9.6.3. Solving Two Equations in Two Variables, One Is of the First Degree, and the Other Is of the Second Degree

Determine the solution set of the two equations and rounding the result to the nearest two decimal places if needed.

- A
- B
- C
- D

Determine the dimensions of a rectangle having a perimeter of cm and an area of .

- Acm, cm
- Bcm, cm
- Ccm, cm
- Dcm, cm

The length of a rectangle is cm more than its width. Given that its area is , determine its perimeter.

Show SolutionFind the two points lying on the straight line , where the -coordinate is twice the square of its -coordinate, rounding the result to the nearest two decimal places.

- A
- B
- C
- D

If and , find .

Show SolutionA right triangle has a hypotenuse length of cm and a perimeter of cm. Find the lengths of the other two sides.

- Acm, cm
- Bcm, cm
- Ccm, cm
- Dcm, cm

A car driver moved a distance of km towards the west, then a distance of km towards the south. If the sum of the two distances is km, and the distance between the starting point and the end point is 35 km, find the distance which the driver moved west and that he moved south.

- Akm, km
- Bkm, km
- Ckm, km
- Dkm, km

The age of a father exceeds 2 times the age of his son by 14 years, and the sum of the squares of their ages exceeds 4 times the product of their ages by 4. Find their ages.

- A the father's age years, the son's age years
- B the father's age years, the son's age years
- C the father's age years, the son's age years
- D the father's age years, the son's age years

The difference between the perimeters of two square-shaped pieces of land is 12 metres and that between their areas is 45 square metres. Find the side length of each of them.

- A6 metres, 9 metres
- B12 metres, 15 metres
- C9 metres, 12 metres
- D18 metres, 21 metres

In a right-angled triangle, the length of one of the two sides between which the right angle lies is cm less than that of the other, and the hypotenuse is cm long. Find the perimeter to the nearest centimetre.

Show SolutionThe length of a rectangle is cm, its width is cm, and its area is . If its length decreased by cm and its width increased by cm, it will become a square. Find the area of the square.

Show SolutionIn a two-digit number, the units digit is times times the tens digit. Determine the original number, given that the product of the two digits is of its value.

Show SolutionIf the ratio between the perimeters of two squares is , find the ratio between their areas.

- A
- B
- C
- D

Determine the increase in the area of a square when its side length is increased by cm, given that its side length is cm.

- A
- B
- C
- D

Find the two positive numbers whose difference is 1, and the sum of their squares is 113.

- A9, 8
- B11, 10
- C8, 7
- D10, 9

Find the two numbers that one of which is the additive inverse of the other, and the sum of their squares is 72.

- A
- B
- C
- D