Question

The ratio of the length of
two equal sides of a issoseles triangle & the other side is 3:4 .If
the area is 18√5 sq units . then find the other side??​

Answer 1

Answer:

equal sides of issoceles triangles=9

other side = 12

Step-by-step explanation:

given

The ratio of two sides of triangle of issoceles triangle and other side = 3:4

let the triangle be ABC

in which AC=BC=3x

let other side BC = 4x

let D be the mid point of base BC

from pythagoras theorem

hypotense^2=adjacent side ^2+opposite side ^2

AD=height of triangle

(3x)^2=AD^2+(4x)^2

9x^2=AD^2+4x^2

5x^2=AD^2

AD=

$x \sqrt{5}$

Area of triangle =half *base *height

$18 \sqrt{5} = \frac{1}{2} \times 4x ^{2} \sqrt{5}$

$18 \sqrt{5} = 2x \times x \sqrt{5}$

$18 \sqrt{5 } = 2{x}^{2} \sqrt{5}$

${x }^{2} = 9$

$x = 3$

AB= 3x

AB =3×3

AB=9

BC=4x

BC=4×3

BC=12