Question

A triangle and parallelogram have same area.the sides of traingle are 48, 20, 52cm.base of parallelogram is 20 cm.find area of traingle using herons formula.the height of the parallelogram

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Area of triangle = Area of parallelogram = 480 sq.cm

Height of parallelogram = 24 cm

Step-by-step explanation:

Sides of triangle (a, b ,c) = 48, 20, 52 cm

Semiperimeter (s) = (a+b+c)/2 = (48+52+20)/2 = 120/2 = 60 cm

Thus, area of triangle by heron's formula

$= \sqrt{s(s-a)(s-b)(s-c)}\\\\= \sqrt{60(60-48)(60-52)(60-20)}\\\\= \sqrt{60 \times 12 \times 8 \times 40}\\\\= \sqrt{230400}\\\\= \bold{480 \: cm^2}$

Base of parallelogram = 20 cm

Let it height be h.

Then, its area = 20h sq.cm

But, area of triangle  = area of parallelogram

Thus, 20h = 480

Or, h = 480/20 = 24 cm

Hence, the height of the parallelogram is 24 cm.