Question

2 12. The perimeter of a triangle is 50 cm. One side of the triangle is 4 cm longer than the smallest side and the third side is 6 cm less than twice the smallest side. Find the area of the triangle. ​

Answer 1

Answer:

To Find:- Area of The Triangle

Solution:-

Let the smallest side be x

third side= 2x-6

second side= x+4

From the data,we can can conclude that it's a scalene triangle,as all 3 sides are different

We know

Area of a scalene triangle

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

Where

s=semi perimeter=perimeter/2

a,b,c= sides

here the perimeter is 50cm

Sum of all sides of a triangle=perimeter

x+(2x-6)+(x+4)=50

4x-2=50

4x=50+2=52

x=52÷4

x=13

Therefore the sides are

x=13cm

2x-6=2×13-6=20cm

x+4=13+4=17cm

Semi Perimeter= 50/2=25

Now,to find area, we've to substitute the values in the formula

$\sqrt{25 (25 - 13)(25 - 20)(25 - 17)} \\ \sqrt{25 \times 12 \times 5 \times 8} \\ 5 \times 2 \times 2 \sqrt{3 \times 5 \times 2} \\ 20 \sqrt{30}$

therefore the Area of the triangle is 20√30cm²

hope it helps

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