Question

The perimeter of a isosceles triangle is 42cm base is 3/2 times each of the equal side find the length of triangle, area of a triangle and height of a triangle.

Answer 1

Heya mate, Here is ur answer
.

Let each equal side be x.

Then base =3/2 of x.

=3x/2.

According to question

Perimeter=42 cm

$x + x + \frac{3x}{2} = 42$

$\frac{2x + 2x + 3x}{2} = 42$

$\frac{7x}{2} = 42$

By Cross multiplication

7x=42×2

$x = \frac{42 \times 2}{7}$

$x = 6 \times 2$

x=12

So,each equal side =12 cm

Base =3x/2

=3×12/2

=3×6

=18 cm

Area of triangle=?

$s = \frac{12 + 12 + 18}{2}$

$s = \frac{42}{2}$

s=21

Area of ∆=

$\sqrt{s(s - a)(s - b)(s - c)}$


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


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

$= \sqrt{7 \times 3 \times 9 \times 9 \times 3}$

$= 9 \times 3 \sqrt{7}$

$= 27 \sqrt{7} cm {}^{2}$

Height=?

Area of ∆=1/2×base×height

$27 \sqrt{7} = \frac{1}{2} \times 18 \times height$

$27 \sqrt{7} = 9 \times height$

$\frac{27 \sqrt{7} }{9} = height$

$3 \sqrt{7} = height$


Warm regards

@Laughterqueen

◦•●◉✿[Tʜᴀɴᴋ ʏᴏᴜ]✿◉●•◦

Be Brainly ✌✌✌