Question
Download Solution PDFThe area of a triangle is 480 cm2 and the ratio of its sides is 10 ∶ 24 ∶ 26. What is the perimeter of the triangle?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven-
Ratio of length of sides = 10 : 24 : 26
Area = 480 cm2
Concept Used-
Heron's Formula-
Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is -
where s = Semi-perimeter of the triangle
Calculation-
Let the length of the triangle be 10x, 24x and 26x.
Semiperimeter = (10x + 24x + 26x)/2
⇒ 30x
According to Question -
√{30x(30x - 10x)(30x - 24x)(30x - 26x)} = 480
⇒ √(30 × 20 × 6 × 4 × x4) = 480
⇒ 120x2 = 480
⇒ x2 = 4
⇒ x = 2
Now,
10x + 24x + 26x = 60x
⇒ 120 cm
∴ The perimeter of the triangle is 120 cm.
Shortcut TrickRecognize that the given triangle has side lengths in the ratio 10:24:26.
That is it is a triplet, hence it is a right-angle triangle.
⇒ Use the formula for the area of a triangle:
⇒ Area = (base * height) / 2.
Given that the area is 480 cm²,
⇒ Let's assume the base is 10x and the height is 24x,
⇒ (10x × 24x) / 2 = 480.
⇒ x2 = 4
⇒ x = 2
Calculate the perimeter of the triangle by summing the side lengths:
10x + 24x + 26x = 60x.
⇒ 60 × 2 = 120
Therefore, the perimeter of the triangle is 120 cm
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