One side of
a right angled triangle is 12 m. Difference of its hypotenuse and the
other side is 8m ,
then find the lengths of the two sides and its area. Verify the
Heron's formula
Answers
given :-
one of the side of the right angle triangle = 12m
ATQ, difference between it's hypotenuse and the other side is 8m.
let the other side of the triangle be x.
therefore it's hypotenuse = x + 8
by Pythagoras theorem we get,
➡ h² = b² + p²
➡ (x + 8)² = (x)² + (12)²
➡ x² + 16x + 64 = x² + 144
➡ 16x = 144 - 64
➡ 16x = 80
➡ x = 80/16
➡ x = 5m
hence, the other side = x = 5m and it's hypotenuse is = x + 8 = 13m
area of the triangle = 1/2 × b × h
= 1/2 × 5 × 12
= 5 × 6
= 30cm²
now to find it's area by heron's formula, we needa find it's semi-perimeter
semi-perimeter = (5 + 12 + 13)/2
= 30/2
= 15m
it's area = √s(s - a)(s - b)(s - c)
= √[15(15 - 5)(15 - 12)(15 - 13)]
= √(15 × 10 × 3 × 2)
= √(3 × 5 × 2 × 5 × 3 × 2)
= √(2 × 2 × 3 × 3 × 5 × 5)
= 2 × 3 × 5
= 30cm²
hence verified!
Answer:
5m,13m,30cm^2
Step-by-step explanation:
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