Answer :
The value of n is 15.The width of the right angled triangle is n + 3 cm while its height is 5 cm less than its width. We have to find the value of n.
Given that,Area of the right angled triangle = 120 cm²Width of the triangle = n + 3 cm Height of the triangle = width - 5 cm Area of the right angled triangle = (1/2) × base × height. Here, the base of the triangle is the width of the triangle, and the height of the triangle is the height of the triangle.So,120 cm² = [tex](1/2) × (n + 3) × (n + 3 - 5)120 cm² = (1/2) × (n + 3) × (n - 2)[/tex]
Multiplying both sides by 2,240 cm² = (n + 3) × (n - 2)
Expanding the right hand side of the equation,n² + n - 6 = 240n² + n - 246 = 0
Solving for n by using quadratic formula,we get,n = ( -1 + √(1 + 4 × 246 × 1))/2 × 1 or n = ( -1 - √(1 + 4 × 246 × 1))/2 × 1n = 15 or n = - 16Discarding the negative value of n, the value of n is 15 cm.
The width of the right angled triangle is n + 3 cm while its height is 5 cm less than its width. We have to find the value of n.Given that,Area of the right angled triangle = 120 cm²Width of the triangle = n + 3 cmHeight of the triangle = width - 5 cmArea of the right angled triangle = (1/2) × base × heightHere, the base of the triangle is the width of the triangle, and the height of the triangle is the height of the triangle.So,120 cm² = (1/2) × (n + 3) × (n + 3 - 5)120 cm² = (1/2) × (n + 3) × (n - 2)Multiplying both sides by 2,240 cm² = (n + 3) × (n - 2)Expanding the right hand side of the equation,n² + n - 6 = 240n² + n - 246 = 0Solving for n by using quadratic formula,we get,n = ( -1 + √(1 + 4 × 246 × 1))/2 × 1 or n = ( -1 - √(1 + 4 × 246 × 1))/2 × 1n = 15 or n = - 16Discarding the negative value of n, the value of n is 15 cm. Therefore, the value of n is 15.
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