How to make word problems into quadratic equations?

Steps involved in solving a word problem:

1. Write what is given and what is required.
2. Denote the unknowns by the variables as x, y, etc.
3. Change the problem into a problem of mathematical statements.
4. Form the quadratic equation in two variables using the conditions given in the problems.
5. Solve the equations for the unknowns.

Example:

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle.

Given:

The height of a right triangle is $7\ cm$ less than its base. The hypotenuse is $13\ cm$.

To do:

We have to form the quadratic equation to find the base of the triangle.

Solution:

Let the length of the base be $x\ cm$.

The height of the triangle $=x-7\ cm$

Using the Pythagoras theorem,

$(x)^2+(x-7)^2=(13)^2$

$x^2+x^2+49-14x=169$

$2x^2-14x+49-169=0$

$2x^2-14x-120=0$

$x^2-7x-60=0$

$x^2-12x+5x-60=0$

$x(x-12)+5(x-12)=0$

$(x-12)(x+5)=0$

$x=12$ or $x=-5$

Length cannot be negative. Therefore, $x=12\ cm$.

The required equation is $x^2-7x-60=0$, the length of the base is $12\ cm$ and the height of the triangle is $(12-7)=5\ cm$.

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Updated on: 10-Oct-2022

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