Question

1.

In AXYZ, |XZ| = 13 cm, XY = 12 cm and
ZXYZ = 90°. Find YZ if the area of the
triangle is 30 cm².

Answer 1

Explanation:

I think you mean triangle XYZ. and angle XYZ.

so, the angle at Y is 90°.

that makes XZ the Hypotenuse (baseline opposite of the 90° angle) of the right-angled triangle.

so, we can actually use Pythagoras (we don't need the area of the triangle to solve) :

13² = 12² + YZ²

169 = 144 + YZ²

25 = YZ²

YZ = 5 cm

just to check - the area of this triangle is (remember, it is a right-angled triangle, so XY and YZ serve also as baseline and height) :

area = 12 × 5 / 2 = 60/2 = 30 cm²

correct, it fits.