Algebra/Geometry?

Question

The base of a triangle is 4 centimeters longer than the altitude. The area of the triangle is 30 square centimeters.

a) what is the length of the base?

b) what is the length of the altitude?

Answer 1

Let a = altitude

Then base = a + 4

area = 0.5 base * altitude

30 = 0.5 a(a + 4)

a² + 4a = 60

a² + 4a - 60 = 0

(a - 6)(a + 10) = 0

a = 6, -10

Since -10 is a trivial solution

a = 6 cm (altitude)

a + 4 = 10 cm (base)

.

Answer 2

let us assume the altitude of the triangle as 'x'

Given that base is 4 cm loger than the side, so

base = x + 4

Area of the triangle is = 1/2 (bh)
30 sq.cm = 1/2 (x) (x+4)

multiplying 2 on both sides we get

60 = x^2 + 4x

solving for x gives

x = 6 and -10

Since the side cannot be negative we take x as 6 cm.

So the Altitude of the triangle = 6cm

Base = altitude + 4 = 6 + 4 = 10 cm

Answer 3

Hi,

Let 'x' cm be the Altitude
Then Base = (x + 4) cm (Given)
Area of Triangle = (1/2) X Base X Altitude
= (1/2) x (x+4) = 30 sq. cm (Given)
x(x + 4) = 60
x^2 + 4x - 60 = 0, this is of the form of quadratic equation ax^2 + bx +c = 0

There are two ways to solve this problem

First method: solving Quadratic equation for x
---------------------------------------------------------------
The solution is given by,
x = (- b +/- (b^2 - 4ac))^(1/2)/2a,
On substituting values of a = 1, b = 4 and c = - 60, we get
x = (-4 +/- ( 4^2 - 4 (1) (- 60)))^(1/2)/2(1)
= (- 4 +/- (256)^(1/2)/2
= (- 4 + 16)/2 and (- 4 -16)/2
= 6 and -10, as the value of altitude can not be negative
Altitude= 6 cm
There for Base = 10 cm

Secnd Method: Factorization
----------------------------------------

x^2 + 4x - 60 = 0
x^2 + 10x - 6x - 60 = 0
x(x + 10) - 6(x + 10) = 0
(x + 10)(x - 6) = 0, that is
x + 10 = 0 and or x - 6= 0, that is
x = - 10 and or x = 6
As the Altiutude shouild have positive value,
x = Base = 6 cm
Altitude = (x + 4) = 10 cm

Depending upon which chapter your appeared adapt one of the above solutions.

If you want a general method to solve by factorization, refer to my earlier answer at
http://answers.yahoo.com/question/index;_ylt=ArkdgOIz3oA.gpdAmhGgVVbty6IX?qid=20070516215828AA0hjNG&show=7#profile-info-HXVjfdjPaa

Good luck

Answer 4

altitude is 6 and base length is 10

Answer 5

MATH..............EEEEEEEEK!!!!!!!:-O