The Smallest side of a right angled triangle is 13 cm less than the side of a square of perimeter 72 cm. Second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm. What is the largest side of the right angled triangle?Choices:- 14 13 12 11
Question
The Smallest side of a right angled triangle is 13 cm less than the side of a square of perimeter 72 cm. Second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm. What is the largest side of the right angled triangle?Choices:- 14 13 12 11
Solution
Sure, let's solve this step by step:
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The perimeter of a square is given by 4 * side. So, the side of the square is 72 cm / 4 = 18 cm.
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The smallest side of the right angled triangle is 13 cm less than the side of the square, so it's 18 cm - 13 cm = 5 cm.
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The area of a rectangle is given by length * breadth. So, the length of the rectangle is 112 cm² / 8 cm = 14 cm.
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The second largest side of the right angled triangle is 2 cm less than the length of the rectangle, so it's 14 cm - 2 cm = 12 cm.
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In a right angled triangle, the largest side (hypotenuse) can be found using the Pythagorean theorem: a² + b² = c². Here, a and b are the two smaller sides and c is the hypotenuse. So, c = sqrt(a² + b²) = sqrt((5 cm)² + (12 cm)²) = sqrt(25 cm² + 144 cm²) = sqrt(169 cm²) = 13 cm.
So, the largest side of the right angled triangle is 13 cm.
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