Question

3. The length of a side and the corresponding height
of a triangle are (x+3) cm and (2x – 5) cm respectively.
Given that the area of the triangle is 20 cm², find
the value of x.
​

Answer 1

Answer:

x=(11/2) or 5.5 cm

Step-by-step explanation:

Area of triangle= $\frac{1}{2}$×base×height

Given,

base=x+3

Height=2x-5

Area of triangle=20

⇒20=(1/2)(x+3)(2x-5)

⇒40=2x²-5x+6x-15

⇒55=2x²+x

⇒2x²+x-55=0

⇔x=(-1±√1+440)/4

=-(1±21)/4

=(22/4) or -(20/4)

∴x=(11/2) or 5.5 cm [∵length cannot be negative]