Question

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The perimeter of a right triangle is 550m. If its sides are in the ratio 12 : 11 : 7. Find the area of the triangle.​

Answer 1

Question

The perimeter of a right triangle is 550m. If its sides are in the ratio 12 : 11 : 7. Find the area of the triangle.

Solution

Given :-

• Perimeter of right triangle = 550 m
• Ratio of side be = 12 : 11 : 7

Find :-

• Area of right triangle

Explanation

Important Formula

★ Perimeter of triangle = Sum of all side

★ Area of right triangle = (1/2) * Base *

Height

________________________

Let,

In Right ∆ PQR

Side be ,

• PQ = 12x.
• QR = 11x
• RP = 7x

So,

==> Perimeter of right triangle = 550

==> PQ + RQ + RP = 550

==> 12x + 11x + 7x = 550

==> 30x = 550

==>x = 550/30

==> x = 55/3

Then,

==> Side of PQ = 12x = 12 × 55/3 = 220 m

==>Side of QR = 11x = 11 × 55/3 = 605/3 m

==> Side of RP = 7x = 7 × 55/3 = 385/3 m

___________________________

In Right ∆ PQR,

• Hypotenuse (PQ) = 220 m
• Perpendiculer (QR) = 605/3 m( Height)
• Base (RP ) = 385/3 m

So, Now Calculate Area of Right Triangle

==> Area of Right Triangle = 1/2 * 385/3 * 605/3

==> Area of Right Triangle = 2,32,925/18

==> Area of Right Triangle = 12,940.277 m²

___________________________

Hence

• Area of Right Triangle be = 12,940.277 m²

__________________

Answer 2

GiveN :-

$\bigstar$ The perimeter of a right triangle is 550 m.

$\bigstar$ Its sides are in the ratio 12 : 11 : 7.

TO DeterminE :-

The area of the triangle.​

AcknowleedgemenT :-

Let the sides of the triangle be 12x, 11x and 7x.

$\bigstar$ Perimeter of the triangle = sum of all the sides

$\bigstar$ Area of the triangle = 1/2 × Base × Height

$\bigstar$ (Hypotenuse)² = (Perpendicular)² + (Base)²

(in a right angle triangle only)

SolutioN :-

Perimeter of the triangle = 12x + 11x + 7x = 550 cm

⇒30x = 550

⇒x = 550/30

⇒x = 55/3

Now, the sides are :-

$\sf{12x=12\times \dfrac{55}{3} }\\\\\sf{=4\times 55}\\\\\sf{=220\ cm}$

$\rule{100}2$

$\sf{11x=11\times \dfrac{55}{3} }\\\\\sf{=\dfrac{605}{3}\ cm }$

$\rule{100}2$

$\sf{7x=7 \times \dfrac{55}{3} }\\\\\sf{=\dfrac{385}{3}\ cm }$

$\rule{100}2$

We know,

in a right angle triangle, the hypotenuse is the longest side. Out of all the sides obtained, 220 is the longest length.

(Refer to the attachment for the diagram)

Let the other 2 sides be considered as base and perpendicular(height).

Now,

$\sf{Area=\dfrac{1}{2}\times base\times height }$

$\sf{\implies Area=\dfrac{1}{2} \times \dfrac{605}{3} \times \dfrac{385}{3} }$

$\sf{\implies Area=\dfrac{232925}{18} }\\\\\boxed{\sf{\implies Area=12940.277\ cm^2}}\:\:\:\:\:\:\:\: \mathbf{\cdots ANSWER}$