Question

Sidea of a triangle are in ratio 5:3:3. Perimeter of the triangle is 110cm. Find the area of rhe triangle

Answer 1

Answer:-

Ratio of the sides of the triangle : 5:3:3

Perimeter of the Triangle : 110 cm

Let the,

First Side : 5x

Second One : 3x

Third One : 3x

According to the Question:-

5x + 3x × 2 = 110 (Note: We wrote ×2 because 3x is in the equation two times)

=> 5x + 6x = 110 (Multiplication of 3x by 2)

=> 11x = 110 (Addition of both like terms)

=> x = 110/11 = 10

Hence, we got the value:

x = 10

Therefore, the sides are:-

First One : 5 × 10 = 50 cm

Second One : 3 × 10 = 30 cm

Third One : 3 × 10 = 30 cm

(Note: Together they make 110 cm)

We know,

Area of Triangle - 1/2 × base × height

Hence,

1/2 × 50 × 30

1/2 × 50 × 30=> 25 × 30

1/2 × 50 × 30=> 25 × 30=> 750 cm²

REQUIRED ANSWER:-

The area of the triangle is 750 cm².

Answer 2

Question :

Sides of a triangle are in the ratio 5:3:3. Perimeter of the triangle is 110 cm. Find the area of the triangle.

Solution :

$\underline {\bold {Given:}}$

• Sides of the triangle in the ratio = 5:3:3
• Perimeter of the triangle = 110 cm.

$\underline {\bold {To\:Find:}}$

• The area of the triangle.

Let the sides of the triangle be 5 x cm, 3x cm and 3x cm.

$\fbox {\pink {Perimeter \:of\: triangle =Sum \:of\: all\: three\: sides}}$

$\implies Perimeter \:of\: triangle =Sum \:of\: all\: three\: sides \\ \implies 110 = 5x + 3x + 3x \\ \implies110 = 11x \\ \implies \frac{110}{11} = x \\ \implies10 = x \\ \implies x = 10$

$\therefore {First\: side =(5\times 10)\:cm=50\:cm}$

$\therefore {Second \:side =(3\times 10)\:cm=30\:cm}$

$\therefore {Third\: side =(3\times 10)\:cm=30\:cm}$

$\boxed {\blue{Area\: of\: triangle = \frac{1}{2}\times base\times height}}$

Taking : First side =50 cm as base .

Taking : Second side=30 cm as height.

$\implies Area\: of\: triangle = \frac{1}{2}\times base\times height\\\implies Area\: of\: triangle = \frac{1}{2}\times 50 \:cm\times 30\:cm\\ \implies Area\: of\: triangle=1\times 25\:cm\times 30\: cm\\\implies Area\: of\: triangle=750\:cm^2$

$\boxed{\green {The\:area\: of\:the \:triangle = 750\:cm^2}}$

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