The sides of a triangle are in the ratio 10: 24:26 and its perimeter is 300 m. What is its are
Answers
Answer:
Step-by-step explanation:
The given ratio is 10:24:26. Hence, lets assume that the sides are a= 10x, b=24x, and c=26x.
Perimeter = 300 = 10x + 24x + 26x = 60 x
Solving for x, we get x=5.
So, the sides are a=50, b=120, c=130.
One important thing to notice is that the the sides are in the ratio of Pythagorean triplets. In this case, 5:12:13.
So, this is a right angled triangle, where c=130 is the hypotenuse.
Hence, the area(A) = (1/2)* base * height
A = (1/2) * 120 * 50 = 3000 sq m.
Method 2:
Perimeter = 300 = 10x + 24x + 26x = 60 x
Solving for x, we get x=5.
So, the sides are a=50, b=120, c=130.
Using the direct formula to find Area(A) of right angled triangle, where P is known.
A = P*y[(P-2y)/4(P-y)]
Please note that ‘y’ can be either height or base, i.e. either a=50 or b=120 in this case.
If we consider ‘a’, then A = P*a[(P-2a)/4(P-a)]
Substituting a= 50, A=300*50[(300–2*50)/4(300–50)] = 3000
Similarly for b , where b= 120, A=300*120[(300–2*120)/4(300–120)] = 3000
Answer:
The sides of a triangle are in the ratio 10: 24:26 and its perimeter is 300 m. then its area = 3000 sq.units.
Step-by-step explanation:
The given proportion is 10:24:26. Consequently, lets expect that the sides are a= 10x, b=24x, and c=26x.
perimeter = 300 = 10x + 24x + 26x = 60 x
Tackling for x, we get x=5.
Thus, the sides are a=50, b=120, c=130.
Something significant to see is that the sides are in the proportion of Pythagorean trios. For this situation, 5:12:13.
Thus, this is a right calculated triangle, where c=130 is the hypotenuse.
Consequently, the area(A) = (1/2) * base * lheight
A = (1/2) * 120 * 50 = 3000 sq m.
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