Geometry Word problem

Question

The height of a triangle is 11 inches more than twice the length of the base. If the area of the triangle is 108 square inches, find the base and height of the triangle.

Answer 1

The formula for the area of a triangle is A = 1/2 b h

Let the base be b.

Then, h = 2 b + 11

The area of the triangle is 1/2 b h =

1/2 b (2b + 11) =b^2 + 11/2 b

b^2 + 11/2 b = 108

b^2 + 11/2 b - 108 = 0

To not have fractions, 2b^2 + 11b - 216 = 0

(b - 8) (2b + 27) = 0

b = 8, -27/2

Clearly, a negative root makes no sense, so b = 8

As a check 1/2(8)(2*8+11) = 1/2(8)(27) = 108

Answer 2

Hi Haaziq ,

First of all, draw a triangle and choose h as a height and base as b

second, make an equation between h and b: h = 11 + 2 b

Third, you know the area and also you know how you can find it ( correct?)

area = 1/2 h b = 108 inch²

Now, replace h in this formula, it means----> 1/2 ( 11+ 2 b ) b = 108

only you need to solve this equation by quadratic formula

1/2 ( 11+ 2 b ) b = 108 both side times 2

( 11+ 2 b ) b = 216

2b² + 11b -216 = 0 -----> b = 8 inches and b = -54/4 unacceptable

h = 11 + 2b = 11 + 2(8) = 27 inches

you can prove area = 1/2 h b 1/2 *8*27 = 108!!!!

I hope it is useful,

Minoo

Answer 3

Based on the wording the equation is as follows.

h = 11 + 2b "height of triangle is 11 inches more than twice the base"

A = (1/2)bh =108 "area of a triangle half base times height

By solving the equation h = 11 + 2b for the base, you will get b = (h -11)/2.

If we substitute b = (h -11)/2 into the Area equation, you will get A = (1/2)((h -11)/2)h

Doing some algebra (distributive property), you will get A = (h² -11h)/4 = 108

Using the equation (h² -11h)/4 =108 to get rid of a fraction multiply be denominator 4

You have h² -11h = 432, this is a quadratic h² -11h -432 = 0.

When you solve this quadratic by graphing in desmos (where it crosses x axis) you will get 27.

So h = 27. Now you use the original equation h = 11 + 2b to get 27 = 11 + 2b and solve the equation for b.

Answer 4

GIVEN : h = 2b + 11

Area=108 sq. inches

TO FIND : h=? b=?

SOLUTION : A => 1/2 * b * h = 108

1/2 * b * (2b +11) =108

2b^2 + 11b = 108 *2

2b^2 + 11b - 216=0

2b^2-16b + 27b -216 =0

2b(b-8) + 27(b-8) = 0

(b-8) (2b+27) = 0

b-8 = 0

b = 8 inches

h = 2b + 11

h = 2*8 + 11

h = 16 + 11

h = 27 inches