Question

Mathema
8. Leg XY of the right triangle shown in the
diagram below is twice as long as
leg YZ.
Z
Y
х
If the area of the triangle is 36 cm?, what
is the length, in cm, of leg XY?
(1)
6
(2)
9
(3)
12
(4)
18
(5)
24

Answer 1

9514 1404 393

Answer:

  (3)  12

Step-by-step explanation:

Let x represent the length of leg XY. Then the length of YZ is x/2 and the area  of the right triangle is ...

  A = 1/2bh

  A = 1/2(x)(x/2) = x²/4

  36 = x²/4 . . . . . use the given value for area

  144 = x² . . . . . . multiply by 4

  √144 = 12 = x . . . . . take the square root

The length of leg XY is 12 cm.