Question

Calculate the perimeter of the triangle and show that it is 23.5 cm, correct to 1 decimal place.

Show all your working.

Answer 1

The triangle's area is
`200 cm^2` and its perimeter is 58.1 cm (rounded to 1 decimal place).

To calculate the area of the triangle, we can use the formula:

Area of a triangle = 1/2 * base * height

In this case, the base of the triangle is 10 cm and the height is 40 cm. Therefore, the area of the triangle is:

Area of triangle = 1/2 * 10 cm * 40 cm =
`200 cm^2`

To calculate the perimeter of the triangle, we need to add the lengths of all three sides. The lengths of the two sides are given in the image (10 cm and 23.5 cm). To find the length of the third side, we can use the Pythagorean theorem:

`a^2 + b^2 = c^2`

Where a and b are the lengths of the two sides we know, and c is the length of the third side we want to find.

In this case, we have:

`10^2 + 23.5^2 = c^2\\c^2 = 605\\c =\sqrt{(605)`

c = 24.6 cm (approximately)

Therefore, the perimeter of the triangle is:

Perimeter of triangle = 10 cm + 23.5 cm + 24.6 cm = 58.1 cm

Answer:

(i) The area of the triangle is
`200 cm^2.`

(ii) The perimeter of the triangle is 58.1 cm, correct to 1 decimal place.

Working:

(i) To calculate the area of the triangle, we used the formula:

Area of a triangle = 1/2 * base * height

In this case, the base of the triangle is 10 cm and the height is 40 cm. Therefore, the area of the triangle is:

Area of triangle = 1/2 * 10 cm * 40 cm =
`200 cm^2.`

(ii) To calculate the perimeter of the triangle, we needed to find the length of the third side, which we did using the Pythagorean theorem:

`a^2 + b^2 = c^2`

Where a and b are the lengths of the two sides we know, and c is the length of the third side we want to find.

In this case, we had:

`10^2 + 23.5^2 = c^2\\c^2 = 605`

`c = \sqrt{(605)`

c = 24.6 cm (approximately)

Therefore, the perimeter of the triangle is:

Perimeter of triangle = 10 cm + 23.5 cm + 24.6 cm = 58.1 cm

Conclusion:

The area of the triangle is
`200cm^2` and the perimeter of the triangle is 58.1 cm, correct to 1 decimal place.