Question

the perimeter of an isoceles triangle is 42 cm and its base is 3/2 times each of the equal sides. find the length of each side of a triangle,area of the triangle and the height of the triangle

Answer 1

LET THE LENGTH OF EQUAL SIDES BE X.
BASE=3/2x..........................(GIVEN)
PERIMETER OF TRIANGLE=42cm..(given)
$x + \frac{3}{2} x + x = 42$

$\frac{2x + 3x + 2x}{2} = 42.........lcm$
$\frac{7x}{2 } = 42$
$7x = 42 \times 2$
$7x = 84$
$x = 12cm$

SIDES OF THE TRIANGLE:
x=12cm,3/2x=3/2×12=18cm,x=12cm
12cm,18cm&12cm

WE HAVE TO FIND THE AREA OF TRIANGLE

BUT WE DON'T HAVE THE HEIGHT OF IT SO?

HERE WE HAVE ALL THE THREE SIDES SO HERE WE MAY USE HERONS FORMULA!!!

THE OTHER PART OF THE SOLUTION IS GIVEN IN THE PIC.

SO , ACCORDINGLY, THE AREA OF TRIANGLE IS 27√7 sq. cm
THE HEIGHT OF THE GIVEN TRIANGLE IS 3√7cm.

HOPE THIS HELPS YOU!!!

THE QUESTION IS FROM STD 9TH STD RIGHT

THE QUESTION WAS INTERESTING !!!