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Altitude CH and area of triangle ABC

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October 24, 2005
geometrysimilar trianglesPythagorean Theorem

Problem Statement

A right triangle ABCABC with hypotenuse ABAB has side AC=15AC = 15. Altitude CHCH divides ABAB into segments AHAH And HBHB, with HB=16HB = 16. The area of ABC\triangle ABC is: [asy] size(200); defaultpen(linewidth(0.8)+fontsize(11pt)); pair A = origin, H = (5,0), B = (13,0), C = (5,6.5); draw(C--A--B--C--H^^rightanglemark(C,H,B,16)); label("AA",A,W); label("BB",B,E); label("CC",C,N); label("HH",H,S); label("1515",C/2,NW); label("1616",(H+B)/2,S); [/asy] <spanclass=latexbold>(A)</span>120<spanclass=latexbold>(B)</span>144<spanclass=latexbold>(C)</span>150<spanclass=latexbold>(D)</span>216<spanclass=latexbold>(E)</span>1445<span class='latex-bold'>(A) </span>120\qquad <span class='latex-bold'>(B) </span>144\qquad <span class='latex-bold'>(C) </span>150\qquad <span class='latex-bold'>(D) </span>216\qquad <span class='latex-bold'>(E) </span>144\sqrt5