Question

The height of a triangle is 6 centimeters less than the base. The area of the triangle is 123.5 square centimeters. Find the length of the base and the height of the triangle.

Answer 1

Answer:  

The length of base=19cm

The length of height=13cm

Given:

Area of the triangle A=123.5$\mathrm{cm}^{2}$

Height of the triangle h=b-6

To find:

Length of the base

Length of the height

Step by Step Explanation:

Solution:

According to the formula, Area of the triangle

$\mathrm{A}=\frac{1}{2} b \times h$

Where b=Base of the triangle

h=Height of the triangle

We know the value of A=123.5$\mathrm{cm}^{2}$ and also we know

h=b-6

Substitute these values in the above equation we get

123.5=$\frac{1}{2} b \times(b-6)$

247=$b^{2}-6 b$

$b^{2}-6 b-247=0$

The above equation is of the form

$A x^{2}+B x+C=0$

Compare the above two equations we get

A=1, B=-6, C=-247

$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\frac{-(-6) \pm \sqrt{(-6)^{2}-4(1)(-247)}}{2(1)}$

$\frac{6 \pm \sqrt{36+4(247)}}{2}$

$\frac{6 \pm \sqrt{36+988}}{2}$

$\frac{6 \pm \sqrt{1024}}{2}$

$\frac{6 \pm 32}{2 a}$

$\frac{6+32}{2}OR\frac{6-32}{2}$

38/2 OR -26/2

The value of b can't be negative so we take

b=38/2=19cm

Though we know that

h=b-6=19-6=13cm

Result:

Thus the length values of b and h are 19 and 13 cm respectively