Question

4 A triangle with a height of 3 cm and a base

of x cm is the result of reducing each
dimension by a scale factor of one-third.
The area of the original triangle is
162 cm². What was the original length of
the base?

Answer 1

L = 36

Explanation:

"A triangle with a height of 3 cm and a base of x cm is the result of reducing each dimension by a scale factor of one-third"

We are looking for the original. This triangle was reduced by 1/3, so we would have to mulitply by 3 to get the original triangle measurements.

height = 3 x 3 = 9

length = x * 3

"The area of the original triangle is 162 cm²."

Area = Base x Height/2

162 = (x*3) * 9/2

324 = (x*3)*9

36 = x*3

x = 12

What was the original length of the base?"

Length = x * 3

= 12 * 3

Length = 36

I hope this helped!