The height of a triangle is 5 centimeters greater than the base. The area of the triangle is 375 square centimeters. Find the length of the base and the height of the triangle

Using the area formula for a triangle, you can solve for the length of the base and height. Since A = (base * height) / 2, we can rearrange to solve for the length of the base or the height. I will be solving for the length first.

Using the formula given, you can rearrange it to find that the base equals

B=2A/H

Remembering that the height is 5 cm greater than the base, we can say H=B+5

plugging that value in for H, we get that

B=2A / (B+5). We know A equals 375, so we can also add that in

B=2 (375) / (B+5)

solving for B will give us a polynomial, by multiplying both sides by B+5 to get

B^2+5B=750. We can bring it all to one side to get

B^2+5B-750=0. solving the polynomial, we get that B equals

(B-25) (B+30) or B=25,-30

Since it doesn't make sense to have a negative length, we can assume it is the 25 value that equals B. Finally we can plug this value into the original triangle area formula to find that

A = (B*H) / 2

2A/B=H

2 (375) / 25=H=30

Base=25cm

Height=30cm

This also fits the criteria of the Height being 5 centimeters greater than tha base value