The area of a right angled triangle is numerically 30 times its height. How long is its base?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 60 unit
The area of a triangle is \(\frac{1}{2}\times\text{base}\times\text{height}\); in a right-angled triangle the two arms at the right angle are the base and the height. The question compares the area with the height, so the height drops out of the equation.
Area is 30 times the height: \(\frac{1}{2}\times b\times h=30h\)
Dividing both sides by the height \(h\) (not zero): \(\frac{1}{2}b=30\)
So the base is \(b=60\)