- The value of x from the figure is 8
- The perimeter of AED is 30.80
To get the value of x, we will use the similarity theorem of the triangle;
a) From the given image:
[tex]\frac{ED}{AD} = \frac{BC}{AC} \\\frac{x}{10} = \frac{x+4}{x+7}\\Cross \ multiply\\x(x+7) = 10(x+4)\\x^2+7x=10x+40\\x^2+7x-10x-40=0\\x^2-3x-40=0[/tex]
On factorizing
[tex]x^2+5x-8x-40=0\\x(x+5)-8(x+5)=0\\(x+5)(x-8) =0\\x=-5 \ and \ 8[/tex]
Since x cannot be negative, then x = 8
b) The perimeter of AED = AE + ED + AD
Given
AD = 10
ED = x = 8
AE² = AD² + ED²
AE² = 10²+8²
AE² = 100 + 64
AE² = 164
AE = √164
AE = 12.80
Perimeter of AED = 12.80 + 8 + 10
Perimeter of AED = 30.80
Hence the perimeter of AED is 30.80.
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