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Find the area and perimeter of a right angled triangle ABC having AC = 13 and BC = 5, sides AB and BC are perpendicular to each other.

Answer:

Given:

AC = 13, BC = 5, AB = ?

Triangle is a right angled triangle.

To find:

Area and perimeter of right angled triangle ABC.

Solution:

By Pythagoras Theorem,

(One side)² + (Other side)² = Hypotenuse²

Therefore,

AB² + BC² = AC²

AB² = AC² - BC² (subtracting BC² from both the sides)

AB² = 13² - 5² (given)

AB² = 169 - 25 (since 13² = 169, 5² = 25)

AB² = 144

Applying square root on both the sides, we get,

AB = 12 (since √144 = 12)

Perimeter of a triangle = Sum of all the sides

Therefore, perimeter of the given triangle ABC = sum of (AB, BC, AC)

= 12 + 5 + 13

= 30 units (since no measuring unit is given)

Area of a right angled triangle

= ½ * Base * Height

= ½ * BC * AB

= ½ * 5 * 12

= 30 sq. units (since no measuring unit is given)

Note: Keep an eye on the measuring unit(s) given in the question, if none is given then do not forget to mention 'units' against your derived answer as shown above, failing to do so may result in deduction of the marks.