Question

Find X and QT. The shape is a Rhombus

Answer 1

Answer:

See below ~

Step-by-step explanation:

Sides of a rhombus are equal.

⇒ QT = TS

⇒ x² - 4x - 10 = 6x + 14

⇒ x² - 10x - 24 = 0

⇒ x² + 2x - 12x - 24 = 0

⇒ x (x + 2) - 12 (x + 2) = 0

⇒ (x + 2)(x - 12) = 0

⇒ x = -2 or x = 12

Substitute both values and see which gives a positive value for QT :

When x = -2 :

• QT = (-2)² - 4(-2) - 10
• QT = 4 + 8 - 10
• QT = 2

When x = 12 :

• QT = (12)² - 4(12) - 10
• QT = 144 - 48 - 10
• QT = 86

The 2 possible answers are :

• x = -2, QT = 2
• x = 12, QT = 86