Question

the sum and difference of two sides of a triangle is 52 cm and 8 cm if the third side of the triangle is 36 cm find the area of the triangle​

Answer 1

Step-by-step explanation:

Answer:16√385 or 313.94267.Right?

Answer 2

To Find :−

$\tt{\implies Area\:_{(triangle)}=?}$

$\sf\small\underline\purple{Solution:-}$

To calculate the area of triangle at first we have find out the sides of triangle. To find the sides of this triangle we have to set up equation. Then find out area of triangle. As given in the question that sum and difference are given so, it's a clue by which you can set up equation. you can easily find out the two sides of triangle by solving them. After that you have to calculate semiperimeter then calculate it's area by applying heron's formula:

$\tt{\implies Sum\:_{(two\: sides)}=52cm}$

$\tt{\implies x+y=52----(i)}$

$\tt{\implies Difference\:_{(two\: sides)}=28cm}$

$\tt{\implies x-y=28-----(ii)}$

Here adding eq (i) and (ii)

$\tt{\implies x+y=52}$

$\tt{\implies x-y=28}$

By solving we get here,

$\tt{\implies 2x=80}$

$\tt{\implies x=40}$

putting the value of x=40 in eq (i)

$\tt{\implies x+y=52}$

$\tt{\implies 40+y=52}$

$\tt{\implies y=52-40}$

$\tt{\implies y=12cm}$

$\tt{\implies Here\: sides\:of\: triangle=12cm,\:36cm,\:40cm}$

$\tt{\implies S=\dfrac{a+b+c}{2}}$

$\tt{\implies a=12,\:b=36,\:c=40}$

$\tt{\implies S=\dfrac{12+36+40}{2}}$

$\tt{\implies S=\dfrac{88}{2}}$

$\tt{\implies S=44cm}$

Now calculate area of triangle:-]

$\tt{\implies A\:_{(triangle)}=\sqrt{s(s-a)(s-b)(s-c)}}$

$\tt{\implies A\:_{(triangle)}=\sqrt{44(44-12)(44-36)(44-4)}}$

$\tt{\implies A\:_{(triangle)}=\sqrt{44*32*8*4}}$

$\tt{\implies A\:_{(triangle)}=\sqrt{(11*4)(8*4)*8*4}}$

$\tt{\implies A\:_{(triangle)}=8*4*2\sqrt{11}}$

$\tt{\implies A\:_{(triangle)}=64\sqrt{11}}$

$\sf\large{Hence,}$

$\tt{\implies Area\:_{(triangle)}=64\sqrt{11}cm^2\:or\:212.26cm^2}$