Question

a rectangle WXYZ having diagonals WY and XZ intersectibg at point U, if in triangle UXY angle Y is 59 then find angle U in triangle WUZ​

Answer 1

Answer:

.

Step-by-step explanation:

Answer

6 cm

Explanation

(Refer attachment for figure)

Given, XYZ is an isoceles triangle, right angled at Y.

XZ = 12 cm

To find,

The length of altitude from Y to XZ

Since, XYZ is an isoceles triangle,

⇒ XY = YZ

Let, XY = YZ = a

Then, applying Pythagoras Theorem, we get

a² + a² = 12²

⇒ 2a² = 12²

Taking root on both sides.

a√2 = 12

⇒ a = 12/√2

Rationalising,

⇒ a = 6√2

Now, area of triangle = 1/2 × base × height

⇒ area of triangle XYZ = 1/2 × XY × YZ

⇒ area of triangle XYZ = 1/2 × 6√2 × 6√2

⇒ area of triangle XYZ = 36 cm²

Let the altitude from Y to XZ be YM

In that case, area of triangle XYZ = 1/2 × XZ × YM

But we know that area of triangle = 36 cm²

⇒ 1/2 × XZ × YM = 36

⇒ 1/2 × 12 × YM = 36

⇒ 6 × YM = 36

⇒ YM = 6 cm

Answer 2

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