Question

The area of a right triangle is 600 $c{m}^2$. If the base of the triangle exceed the altitude by 10 cm, find the dimensions of the triangle.

Answer 1

Let the altitude of the triangle =x cm

base = (x+10) cm

area = 600 sq cm

= 600

x(x+10)= 2 $\times$600

+10x -1200=0

+40x-30x-1200=0

x(x+40)-30(x+40)=0

(x+40)(x-30)=0

x+40=0 or x-30=0

x=-40 or x= 30

x cannot be negative

x=30

base = x+10 =30+10=40

by Pythagoras theorem

$(hypotenuse{)}^2=(base{)}^2+(altitude{)}^2$

=
=1600+900
=2500
hypotenuse =50

three sides of a triangle

30cm,40cm and 50cm