Question

The lengths of the adjacent sides of a parallelogram are 5 centimetres and 12 centimetres. The length of one of its diagonals is 13 centimetres. The area of the parallelogram is :

• A. 400
• B. 169
• C. 40
• D. 60

Answer 1

Answer:

D. 60

Identify the triangle: A diagonal divides a parallelogram into two identical triangles.

The sides of one of these triangles are the two adjacent sides of the parallelogram (5 cm and 12 cm) and the diagonal (13 cm).

Check for a right-angled triangle:

We can use the Pythagorean theorem (a² +b² = c² ) to check if this is a right-angled triangle.

Let a=5 and b=12.

5² +12² =25+144=169

The diagonal's length squared is 13² =169.

Since 5² +12² =13² , the triangle is a right-angled triangle.

This means the two adjacent sides, 5 cm and 12 cm, are perpendicular to each other and serve as the base and height of the parallelogram.

Calculate the area: The area of a parallelogram is given by the formula

A=base × height.

A=12 cm×5 cm

A=60 cm²