It's a right angle triangle and you know one of the sides is 5 cm the other is 3 cm what is the third side
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Step-by-Step Solution
Step 1: Identify the given information
We are given a right-angled triangle with two side lengths: 3 cm and 5 cm. We need to determine if these are the two legs (perpendicular sides) or one leg and the hypotenuse.
Step 2: Apply the Pythagorean Theorem
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs). Here, a and b are the lengths of the legs, and c is the length of the hypotenuse.
Step 3: Case 1: Given sides are legs
If the given sides, 3 cm and 5 cm, are the legs of the right-angled triangle, then we can find the hypotenuse c using the Pythagorean theorem. We calculate 32+52=9+25=34. So, c2=34, which means c=34 cm.
Step 4: Case 2: Given sides are one leg and the hypotenuse
If 5 cm is the hypotenuse and 3 cm is one of the legs, we can find the other leg, a. We set up the equation a2+32=52. This simplifies to a2+9=25, so a2=16. Taking the square root, we find a=4 cm. This is a common Pythagorean triplet (3, 4, 5).