The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000.
1/2b(b + 70) = 3000
Multiply each side by 2
b^2 + 70b = 6000
Subtract 6000 from each side:
b^2 + 70b - 6000 = 0
Using our quadratic calculator, we get:
b = 50 and b = -120
Since the base cannot be negative, we use b = 50.
If b = 50, then h = 50 + 70 = 120
The perimeter is b + h + hypotenuse
Using the right-triangle calculator, we get hypotenuse = 86.02
Adding up all 3 for the perimeter: 50 + 70 + 86.02 = 206.02
- h = b + 70
- A = 1/2bh = 3000
1/2b(b + 70) = 3000
Multiply each side by 2
b^2 + 70b = 6000
Subtract 6000 from each side:
b^2 + 70b - 6000 = 0
Using our quadratic calculator, we get:
b = 50 and b = -120
Since the base cannot be negative, we use b = 50.
If b = 50, then h = 50 + 70 = 120
The perimeter is b + h + hypotenuse
Using the right-triangle calculator, we get hypotenuse = 86.02
Adding up all 3 for the perimeter: 50 + 70 + 86.02 = 206.02