Question

The perimeter of an isosceles triangle is 42cm and it's base is 3/2 times each of the equal sides. Find the area and the height of the triangle.

Answer 1

Answer:

Area = 27 √7 cm²

Step-by-step explanation:

Let the equal sides be ‘a’ cm.

the base = 1.5 * base

base = 3/2 * a

Perimeter = 42 cm ( Given )

a + a + 3/2 * a = 42

7a / 2 = 42

a = 42 * 2 / 7

a = 12 cm

Base = 3/2 * a

Base = 3/2 * 12

Base = 18 cm

Using Heron’s formula,

Area = sqrt ( s * (s-a) * (s-b) * (s-c)),

where s = (a+b+c)/2 and a,b,c are the sides

s = (12 +12+18) /2

s = 21 cm

Area = sqrt (21 * (21-12) *(21–12) * (21–18))

Area = sqrt (21 * 9 * 9 * 3 )

Area = 27 √7 cm²

Answer 2

Step-by-step explanation:

LET X BE THE MEASURE OF THE SIDES.

THEN,

BASE CAN BE 3/2 X

•°• X+X+3/2X=42 cm

7/2X=42

X=42×2/7.

X=12 cm.

NOW,

THE SIDES ARE...

12cm,12cm,18cm

S=1/2(a+b+c)

=1/2(42)

=21cm.

BY USING HERON'S FORMULA,

$\sqrt{21(21 - 12)(21 - 12)(21 - 18)}$

=

$\sqrt{21 \times 9 \times 9 \times 3}$

=71.42 cm^2 (approx.)

NOW,

AREA OF TRIANGLE =71.42cm^2

1/2×18×h=71.42

h=71.42×2/18= 7.937 cm