Question

The perimeter of a triangular field is 240 m. If two of its sides are 50 m and 78 m, find the
perpendicular on the side of length 50 m from the opposite vertex. Also, calculate the cost
at 3.50 per 100 sq m.
with side.

​

Answer 1

hello buddy!!

answer:- Rs.58.8

refer to the above attachment for clear explanation

Answer 2

Solution:

Given:

⇒ Perimeter of triangular field = 240 m.

⇒ Two sides of triangular field = 50 m and 78 m.

To Find:

⇒ Length of perpendicular on side of length 50 m.

⇒ Cost.

Formula used:

$\sf{\implies Perimeter = side\;A+side\;B+side\;C}$

$\sf{\implies Area=\sqrt{s(s-a)(s-b)(s-c)}\;\;\;\;[Heron's\;Formula]}$

$\sf{\implies Area\;of\;triangle=\dfrac{1}{2}\times Base\times Height}$

Now,

$\sf{\implies Perimeter = side\;A+side\;B+side\;C}$

$\sf{\implies 240 = 50 + 78 + side\;C}$

$\sf{\implies 240 = 128 + side\;C}$

$\sf{\implies side\;C = 240 - 128}$

$\sf{\implies side\;C = 112 m}$

Hence, 3rd side is 112 m.

$\sf{Now,\;s=\dfrac{a+b+c}{2}}$

$\sf{\implies s=\dfrac{50+78+112}{2}}$

$\sf{\implies s=\dfrac{240}{2}}$

$\sf{\implies s=120}$

Now, we will find area by using Heron's formula,

$\sf{\implies Area=\sqrt{s(s-a)(s-b)(s-c)}\;\;\;\;[Heron's\;Formula}$

$\sf{\implies Area=\sqrt{120(120-50)(120-78)(120-112)}}$

$\sf{\implies Area=\sqrt{120\times 70\times 42\times 8}}$

$\sf{\implies Area=\sqrt{2822400}}$

$\sf{\implies Area=1680\;m^{2}}$

Hence, Area of Triangular field  is 1680 m².

Now, we will find the length of perpendicular,

$\sf{\implies Area\;of\;triangle=\dfrac{1}{2}\times Base\times Height}$

$\sf{\implies 1680=\dfrac{1}{2}\times 50 \times Height}$

$\sf{\implies 3360=50\times Height}$

$\sf{\implies Height=\dfrac{3360}{50}}$

$\sf{\implies Height=67.2\;m}$

Hence, the length of perpendicular on the side of length 50 m is 67.2 m.

$\sf{Now,\;cost\;is\;3.50\;per\;100\;m^{2}}$

$\sf{\therefore\;cost\;of\;1680\;m^{2}=\dfrac{1680}{100}\times 3.50=Rs.\; 58.8}$

Hence, the cost is Rs. 58.8.