SOLVING GEOMETRIC PROBLEMS USING A SYSTEM OF EQUATIONS WORKSHEET

Problem 1 :

An equilateral triangle has sides of length (3x - y) cm, (x + 5) cm and (y + 3) cm. Find the length of each side.

Solution

Problem 2 :

The figure alongside is a rectangle. Find x and y.

Solution

Problem 3 :

KLM is an isosceles triangle. Find x and y and hence find the measure of the angle at K.

Solution

Problem 4 :

Given that the triangle alongside is equilateral, find a and b.

Solution

Problem 5 :

A rectangle has perimeter 32 cm. if 3 cm is taken from the length and added to the width, the rectangle becomes a square. Find the dimensions of the original rectangle.

Solution

Problem 6 :

The diagonal of the TV screen is 82 cm, and the height is 40 cm. Calculate the width of the screen.

Solution

Problem 7 :

The aspect ratio of the rectangle and its diagonal is 9 : 12 : 15. Calculate the area of the rectangle if the length of the diagonal is 105 cm.

Solution

Problem 8 :

There is a rectangle with the length of 12 cm and diagonal 8 cm longer than the width. Calculate the area of the rectangle.

Solution

Problem 9 :

The length of the sides of the rectangular garden are in the ratio 1 : 2. The connection of the centers of the adjacent sides is 20 m long. Calculate the perimeter of the rectangle.

Solution

Problem 10 :

The dimension of the rectangular plot are (x + 1) m and (2x - y)m. The sum of x and y is 3 m and the perimeter of the plots is 36 m. Find the area of the diagonal of the plot.

Solution

Problem 11 :

The diagonal of the rectangle given below is 36 m. Find the values of x and y.

Solution