1958 AHSME Problems/Problem 31

Problem

The altitude drawn to the base of an isosceles triangle is $8$ , and the perimeter $32$ . The area of the triangle is:

$\textbf{(A)}\ 56\qquad \textbf{(B)}\ 48\qquad \textbf{(C)}\ 40\qquad \textbf{(D)}\ 32\qquad \textbf{(E)}\ 24$

Solution

$[asy] size(300); defaultpen(linewidth(0.8)); pair A=(-1,0),C=(1,0),B=dir(40),D=origin; draw(A--B--C--A); draw(D--B); dot("$ A $", A, SW); dot("$ B $", B, NE); dot("$ C $", C, SE); dot("$ D $", D, S); label("$ 70^\circ $",C,2*dir(180-35)); [/asy]$ $\fbox{}$

1958 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 30	Followed by Problem 32
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1958 AHSME Problems/Problem 31

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