Question

The height of a triangle is 3cm less than twice the base. The area is 10cm2

. Find the base and height.

Answer 1

The base is 4cm and the height is 5cm.

Explanation:

This is a solve the system question. Call H the height of the triangle and B the base. The question tells us:

`H=2B-3`

and

`(B * H)/(2)=10`

Sub the first equation into the second (as H is already isolated). You will end up with a quadratic equation - solve that any way you wish (e.g. quadratic formula). I've provided the factored form below which shows you the roots:

`(B(2B-3))/(2)=10\\(2B^2-3B)/(2)=10\\2B^2-3B=20\\2B^2-3B-20=0\\(2B+5)(B-4)=0\\B= - (5)/(2),4`

In this question, we take B=4. You can't have a negative side length so the other answer is eliminated. Now sub the value for B into either of the original equations. I'll use the first, again because H is already isolated:

`H=2(4)-3\\H=8-3\\H=5`