Question

Δ MAL and Δ DLA are right triangles. If Δ MAL ≅ ΔDLA, then side DL is congruent to side MA, and ∠ MAL is congruent to ∠ DLA. Given ∠ M is 30 °, side DL is (2x + 10) cm, side MA is (3x – 2) cm, and side AL is (x + 5) cm, answer the following questions below:
What is the measurement of DL?

What is the measurement of AL?

What is the measurement of ∠ DLA?

What is the measurement of ∠ AEL?

Answer 1

Answer:

See below.

Step-by-step explanation:

Given :

1. ΔMAL ≅ ΔDLA, DL = MA, ∠MAL = ∠DLA
2. ∠M = 30°
3. DL = (2x + 10) cm
4. MA = (3x - 2) cm
5. AL = (x + 5) cm

To Find :

1. DL
2. AL
3. ∠DLA
4. ∠ADL

Solving :

• DL = MA
• 2x + 10 = 3x - 2
• x = 12
• DL = 24 + 10 = 34 cm

• AL = x + 5
• AL = 12 + 5
• AL = 17 cm

• ∠DLA = 180° - 90° - 30° = 180° - 120° = 60°

• ∠ADL = ∠M = 30°

Answer 2

Answer:

DL = 34 cm

AL = 17 cm

∠DLA = 60°

∠ADL = 30°

Step-by-step explanation:

Given:

• DL = (2x + 10) cm
• MA = (3x - 2) cm

   DL ≅ MA

⇒ 2x + 10 = 3x - 2

⇒ 2x + 12 = 3x

⇒ 12 = x

Substituting found value of x into expressions for DL and AL:

DL = 2x + 10

     = 2(12) + 10

     = 34 cm

AL = x + 5

    = 12 + 5

    = 17 cm

The only way for ΔMAL to be a right triangle, with MA = 34 cm, AL = 17 cm and ∠M = 30° is if

• MA is the hypotenuse
• AL is the shortest side

Given:

• ∠M = ∠D = 30°
• ∠MAL ≅ ∠DLA

Sum of interior angles of a triangle is 180°

⇒ ∠DLA + 30° + 90° = 180°

⇒ ∠DLA + 120° = 180°

⇒ ∠DLA = 60°

As ∠M = ∠D = 30°, then ∠ADL = 30°