Easy and simple triangle area problem

Geometry Level 1

If JAY \triangle \text{JAY} has side lengths 10, 8, and 4, then the area of the triangle can be expressed as a b c \sqrt{\, \overline{abc}\, } , where a b c \overline{abc} is a 3 3 -digit number. Find a + b + c a+b+c .

-6 5 6 7

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6 solutions

Sandeep Bhardwaj
Sep 18, 2014

Using Heron's Formula,

If a,b,c are the three sides of a triangle, then we define s(semi-perimeter) as s = a + b + c 2 s=\dfrac{a+b+c}{2} , then

So here as per given information, let a = 10 , b = 8 , c = 4 a=10,b=8,c=4

A r e a = s ( s a ) ( s b ) ( s c ) Area=\sqrt{s(s-a)(s-b)(s-c)}

= 231 \quad \quad =\sqrt{231}

So a n s w e r = 2 + 3 + 1 = 6 answer=\boxed{2+3+1=6}

did the same

Ganesh Ayyappan - 6 years, 6 months ago

is there any other way . i dont care even if it is little complex.

Guru Prasaadh - 6 years, 5 months ago

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Frankly speaking there are many ways to solve the problem but this is the easiest.Most of these methods involve trigonometry. Example one can use the cosine rule and find the angle between any 2 sides and then use sines to find the area.(ab(sin C)/2)

Sathvik Acharya - 4 years ago
Akshitha Chamala
Jan 17, 2015

We can solve it by herons formulae.

Umer Shairi
Dec 27, 2014

by heros formulae

heron's not heros

Syed Hamza Khalid - 4 years, 1 month ago
Ibraheem Akram
Dec 21, 2014

We can find the area of a triangle by using the Heron's formula . If all the sides of a triangle are give: Area = square root of s(s-a)(s-b)(s-c) Where s= a+b+c/2 here: a=10 ; b=8 ; c=4 So Area = square root of 231 So the Answer is 6.

Ambrish Rathore
Dec 20, 2014

we can easily find the area of any triangle by using Heron's Formula.... Area= square root of s(s-a)(s-b)(s-c).. where s is the (a+b+c)/2.......... by replaing the values we get 231 under the square root......... which is a 3 digit number... so the sum of digits is 2+3+1=6.........

Bhanu Prasad
Dec 20, 2014

let a=8,b=4,c=10; using cosine rule cosC=a^2+b^2-c^2/2ab=-5/16; now sinC=√ (1-cos^2C)=√(231)/16; Area=1/2 a b*sinC=√(231); therefore, a+b+c=2+3+1=6

better option is Heron's formula.......

Ambrish Rathore - 6 years, 5 months ago

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