Question

Could someone please find the value of x and the area please

Answer 1

Answer:

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Answer 2

Since it is a right angle triangle,

By Pythagoras theorem,

(5x - 3)^2 = (2x + 7)^2 + (x + 4)^2

=> 25x^2 - 2.5x.3 + 9 = 4x^2 + 2.2x.7 + 49 + x^2 + 2.x.4 + 16

=> 25x^2 - 30x + 9 = 5x^2 + 28x + 8x + 65

=> 25x^2 - 5x^2 + 9 -65 = 36x + 30x

=> 20x^2 - 56 = 66x

=> 20x^2 - 66x - 56 = 0

Dividing both sides by 2,

=> 10x^2 - 33x - 28 = 0

=> 10x^2 - 40x + 7x - 28 = 0

=> 10x( x - 4) + 7( x - 4) = 0

=> (10x + 7) (x - 4) = 0

Case 1 :

(10x + 7) = 0

=> 10x = -7

=> x = -7/10

Not applicable

Case 2:

(x - 4) = 0

=> x = 4

.•. x = 4

2x + 7 = 8 + 7 = 15 units

x + 4 = 8 units

5x - 3 = 20 - 3 = 17 units

Area of the triangle

= (1/2)*(2x + 7)*(x + 4)

= (1/2)*15*8

= 15*4

= 60 sq. units

Hope it helps you...

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