The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete

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.

• h = b + 70
• A = 1/2bh = 3000

Substitute the height equation into the area equation
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