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olya-2409 [2.1K]
4 years ago
9

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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