Question

(Not drawn to scale)
In right triangle ABC shown, AD = AB and
AE AC. If the area of triangle ADE is 8,
what is the area of triangle ABC?
(A) 10
(B) 15
(C) 20
(D) 24
(E) 30

Answer 1

Step-by-step explanation:

$Given: \\ AD = \frac{4}{5} AB \\ \implies \: AB = \frac{5}{4} AD \\AE = \frac{1}{3} AC \\ \implies \: AC = 3AE \\ Now, \\ A( \triangle ABC ) = \frac{1}{2} \times AB\times AC \\ = \frac{1}{2} \times \frac{5}{4} AD\times 3AE \\ = (\frac{5}{4} \times 3)( \frac{1}{2} \times AD \times AE) \\ = \frac{15}{4} \times A( \triangle ADE ) \\ \{ \because A(\triangle ADE)=8 \:which \:is \:given\} \\ = \frac{15}{4} \times 8 \\ = 15 \times 2 \\ = 30 \: square \: units \\ thus \\ A( \triangle ABC ) = 30 \: square \: units \\ so \: option \: E \: is \: the \: correct \: answer. \\ \\\\ A( \triangle ABC )\: means\: Area\:of\:triangle\:ABC.$