Triangle abc has a perimeter of 22cm. ab=8cm bc=5cm bt calculation, deduce whether triangle abc is a right-angled triangle.

First let's find the length of the last side. We can do this by adding AB and BC together, then subtracting this amount from the perimeter of Triangle ABC, 22 cm.
ABC - (AB + BC) ⇒ 22cm - (8cm + 5cm)
                                    22cm - 13cm = 9cm

The hypotenuse is always the longest side of a triangle, so we know that the side we figured out is the hypotenuse. Now we can use the Pythagorean Theorem to see whether the triangle is a right triangle.

Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse.
If a² + b² do equal c², then the triangle is a right triangle.

8² + 5² = 9²
64 + 25 = 81
89 > 81

The triangle is not a right triangle, but we know that it is obtuse since a and b together are longer than c.

No, ABC is not a right Angled triangle.

Step-by-step explanation:

Given AB = 8, BC = 5

Then AC = 22 - (8 + 5) = 22 - 13 = 9 cm

Using the converse of Pythagoras' identity

If the square of the longest side equals the sum of the squares of the other 2 sides then triangle is right.

AC² = 9² = 81

AB² + BC² = 8² + 5² = 64 + 25 = 89

81 ≠ 89, hence ΔABC is not right- angled

 Second option is correct.

Explanation:

Since we have given that

Total area a farmer has as an orchard = 40 acres

Total area in which he grows apples = 25 acres

Total area on which he grows peaches = 7 acres

Total area on which he grows nectarines = 5 acres

Total area on which he grows plums = 3 acres

According to question, the fruit trees are equally distributed within the orchard,

So,

P( the tree is within the acres of apple trees) is given by

But we have to calculate the Probability that the tree is not within the acres of apple trees,

So, P( the tree is not within the acres of apple trees) is given by

Hence, Second option is correct.