Question

The sides of a quadrilateral are in the ratio 2:3:5:8. The difference between the shortest side and the longest side is 7.5 cm. Work out the perimeter of the quadrilateral.

Answer 1

The perimeter of the quadrilateral is 17.5 cm.

Step-by-step explanation:

To find the perimeter of the quadrilateral, we need to find the lengths of the sides. Let's assume the common ratio is x. So, the sides are 2x, 3x, 5x, and 8x. According to the problem, the difference between the shortest and longest side is 7.5 cm, which means 8x - 2x = 7.5 cm. Simplifying this equation gives 6x = 7.5 cm, and dividing both sides by 6 gives x = 1.25 cm.

Now, we can find the lengths of the sides. The shortest side is 2x = 2(1.25) = 2.5 cm, and the longest side is 8x = 8(1.25) = 10 cm.

The perimeter of the quadrilateral is the sum of all the sides, so the perimeter is 2.5 + 3(1.25) + 5(1.25) + 10 = 17.5 cm.

Answer 2

Step-by-step explanation:

To answer this problem, we may use the information provided about the quadrilateral's side ratio and the difference between the smallest and longest sides.

To begin, we may utilize the difference in length between the shortest and longest sides (7.5 cm) to establish a baseline for one of the sides. We may infer that the shortest side is 7.5 cm and the longest side is (7.5 cm + 7.5 cm) = 15 cm since the difference between the shortest and longest sides is 7.5 cm.

We can calculate the length of the other three sides using the side ratio:

• 3/2 x 7.5 cm = 11.25 cm is the length of the second shortest side.
• 5/2 x 7.5 cm = 18.75 cm is the length of the second longest side.
• 30 cm is the length of the third longest side (8/2 x 7.5 cm).

We sum together all the sides to find the quadrilateral's perimeter:

Perimeter = 67.5 cm = 7.5 cm + 11.25 cm + 18.75 cm + 30 cm

As a result, the quadrilateral's perimeter is 67.5 cm.