Problem 1 :

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Solution :

Let 'x' be the base of the triangle.

Then, altitude is (x - 7).

By Pythagorean Theorem,

132  =  x2 + (x - 7)2

169  =  x2 + x2 - 2(x)(7) + 72

169  =  x2 + x2 - 14x + 49

0  =  2x- 14x + 49 - 169

2x- 14x - 120  =  0

Divide the whole equation by 2

x- 7x - 60  =  0

x- 12x + 5x - 60  =  0

x(x - 12) + 5(x - 12)  =  0

(x + 5)(x - 12)  =  0

x + 5  =  0  or  x - 12  =  0

x  =  -5  or  x  =  12

Because x represents the base of the triangle, it can not take a negative value.

So,

base  =  12 cm

height  =  12 - 7  =  5 cm

Problem 2 :

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article(in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was \$90, find the number of articles produced and the cost of each article.

Solution :

Let 'x' be the number of articles produced on that day.

Then, the cost of production of each article is

=  2x + 3

Total cost of production is

=  number of article x cost of one article

90  =  x(2x + 3)

90  =  2x2 + 3x

2x2 + 3x - 90  =  0

2x2 - 12x + 15 x - 90  =  0

2x(x - 6) + 15(x - 6)  =  0

(2 x + 15)(x - 6)  =  0

2x + 15  =  0  or  x - 6  =  0

x  =  -15/2  or  x  =  6

Because x represents the number of articles, it can not take a negative value.

Then,

x  =  6

So, the number of articles produced is 6.

The cost of each article is

=  2x + 3

=  2(6) + 3

=  12 + 3

=  \$15 Apart from the stuff given in this sectionif you need any other stuff in math, please use our google custom search here.

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