Question

if the ratio of the base and the hypotenuse of a right angled triangle is 4:5 , and the perimeter of the triangle is 48 cm then find its area​

Answer 1

Step-by-step explanation:

AnswEr:-

Area is 96cm².

Step by Step Explanation:-

Given :-

Base : Hypotenuse = 4 : 5

Perimeter = 48cm

To Find :-

Area of the Triangle.

Finding :-

Let us Consider Base and Hypotenuse be 4x and 5x.

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Now, By using Pythagoras theorem :-

Hypotenuse² = Base² + Perpendicular ²

$\longrightarrow\sf\; H^2 = B^2+ P^2$

We know that, Hypotenuse = 5x and Base = 4x.

$:\implies\sf\; P^2= 5x^2 \; - \; 4x^2$

$:\implies\sf\; P^2 = 25x - 16x$

$:\implies\sf\; P = \sqrt{9x^2}$

$:\implies\sf\; P = 3x$

$\large\boxed{\sf{\pink{ P = 3x}}}$

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We know that,

Perimeter = Sum of the all sides

$:\implies\sf\;3x \;+\;4x\;+\;5x$

$:\implies\sf\; 12x$

Given Perimeter is 48 cm.

$:\implies\sf \;12x = 48$

$:\implies\sf\;x = \dfrac{48}{12}$

$:\implies\sf \;x = 4cm$

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Now,

★ Putting the value of x

$:\implies\sf\; Base = 4x$

$:\implies\sf \;4(4) = 16cm$

$:\implies\sf \; Hypotenuse = 5x$

$:\implies\sf \;3(4) = 12cm$

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Formula :-

Area of Triangle :-

$\large\boxed{\sf{\red{\frac{1}{2}\times base\times \; Height}}}$

$:\implies\sf\dfrac{1}{2}\; \times\;16\times\;12$

$:\implies\sf\; Area = 96 cm^2$

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