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4 years ago

What is the length of AC?

Mathematics

1 answer:

adelina 88 [10]4 years ago

3 0

Since both triangles have a right-angle, and the two angles at vertex C are also twins, thus both triangles are similar by AA, therefore,

$\bf \cfrac{small}{large}\qquad \cfrac{DE}{BA}=\cfrac{EC}{CA}\implies \cfrac{7}{84}=\cfrac{x}{156-x}\implies 1092-7x=84x
\\\\\\
1092=91x\implies \cfrac{1092}{91}=x\implies 12=x\qquad \quad \qquad \boxed{AC=156-12}$

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