Question

4. The height of a triangle is 11 more than the base of the triangle. The area of the triangle is 310 cm.

a. Find the height and base of the triangle.
b. Find the area of the triangle. If needed, round to 2 decimal places.
c. Find the perimeter of the triangle. If needed, round to 2 decimal places.

Answer 1

a.

Height = 31 cm

Base = 20 cm

b. 310 cm (given)

c. See Below

Explanation:

a.

Let height be "h" and base be "b"

Area of triangle is:

Area = 0.5 * height * base

THe height is 11 more than base, so we can say:

h = b + 11

So, we have:

Area = 0.5 * b * h

310 = 0.5 * b * (b+11)

Solving for b:

`310 = 0.5 * b * (b+11)\\620=b^2+11b\\b^2+11b-620=0\\(b-20)(b+31)=0\\b=20`

So,

h = 20 + 11 = 31

Height = 31 cm

Base = 20 cm

b.

The area of the triangle is already given as 310 cm

c.

The perimeter is sum of all the sides.

We aren't given whether this is right triangle or not.

So we can't know the third side.

No angle is also given,

Also, the height is one side or perpendicular distance from one vertex to another side, we don't know. So we cannot figure the perimeter out.